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Journal articles on the topic 'Infinite quantum potential-well'

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Author: Grafiati

Published: 4 June 2021

Last updated: 3 February 2022

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1

Gonçalves, A. Oakes O., M. F. Gusson, B. B. Dilem, R. G. Furtado, R. O. Francisco, J. C. Fabris, and J. A. Nogueira. "An infinite square-well potential as a limiting case of a square-well potential in a minimal-length scenario." International Journal of Modern Physics A 35, no. 14 (May 20, 2020): 2050069. http://dx.doi.org/10.1142/s0217751x20500694.

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One of the most widely problem studied in quantum mechanics is of an infinite square-well potential. In a minimal-length scenario its study requires additional care because the boundary conditions at the walls of the well are not well fixed. In order to avoid this we solve the finite square-well potential whose the boundary conditions are well fixed, even in a minimal-length scenario, and then we take the limit of the potential going to infinity to find the eigenfunctions and the energy equation for the infinite square-well potential. Although the first correction for the energy eigenvalues is the same as one found in the literature, our result shows that the eigenfunctions have the first derivative continuous at the square-well walls what is in disagreement with those previous work. That is because in the literature the authors have neglected the hyperbolic solutions and have assumed the discontinuity of the first derivative of the eigenfunctions at the walls of the infinite square-well which is not correct. As we show, the continuity of the first derivative of the eigenfunctions at the square-well walls guarantees the continuity of the probability current density and the unitarity of the time evolution operator.

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2

SUN, GUO-HUA, and SHI-HAI DONG. "NEW TYPE SHIFT OPERATORS FOR THREE-DIMENSIONAL INFINITE WELL POTENTIAL." Modern Physics Letters A 26, no. 05 (February 20, 2011): 351–58. http://dx.doi.org/10.1142/s0217732311034815.

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New type shift operators for three-dimensional infinite well potential are identified to connect those quantum systems with different radials R but with the same energy spectrum. It should be pointed out that these shift operators depend on all variables contained in wave functions. Thus they establish a novel relation between wave functions ψlm(r) and ψ(l±1)(m±1)(r).

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3

Hu, Bambi, Baowen Li, Jie Liu, and Yan Gu. "Quantum Chaos of a Kicked Particle in an Infinite Potential Well." Physical Review Letters 82, no. 21 (May 24, 1999): 4224–27. http://dx.doi.org/10.1103/physrevlett.82.4224.

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4

Kilbane, D., A. Cummings, G. O’Sullivan, and D. M. Heffernan. "Quantum statistics of a kicked particle in an infinite potential well." Chaos, Solitons & Fractals 30, no. 2 (October 2006): 412–23. http://dx.doi.org/10.1016/j.chaos.2006.01.010.

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5

Saputra, Yohanes Dwi. "Quantum Lenoir Engine with a Single Particle System in a One Dimensional Infinite Potential Well." POSITRON 9, no. 2 (December 2, 2019): 81. http://dx.doi.org/10.26418/positron.v9i2.34850.

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Lenoir engine based on the quantum system has been studied theoretically to increase the thermal efficiency of the ideal gas. The quantum system used is a single particle (as a working fluid instead of gas in a piston tube) in a one-dimensional infinite potential well with a wall that is free to move. The analogy of the appropriate variables between classical and quantum systems makes the three processes for the classical Lenoir engine applicable to the quantum system. The thermal efficiency of the quantum Lenoir engine is found to have the same formulation as the classical one. The higher heat capacity ratio in the quantum system increases the thermal efficiency of the quantum Lenoir engine by 56.29% over the classical version at the same compression ratio of 4.41.

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6

EL KINANI, A. H., and M. DAOUD. "COHERENT AND GENERALIZED INTELLIGENT STATES FOR INFINITE SQUARE WELL POTENTIAL AND NONLINEAR OSCILLATORS." International Journal of Modern Physics B 16, no. 26 (October 20, 2002): 3915–37. http://dx.doi.org/10.1142/s0217979202014656.

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This article is an illustration of the construction of coherent and generalized intelligent states which has been recently proposed by us for an arbitrary quantum system.1 We treat the quantum system submitted to the infinite square well potential and the nonlinear oscillators. By means of the analytical representation of the coherent states à la Gazeau–Klauder and those à la Klauder–Perelomov, we derive the generalized intelligent states in analytical ways.

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7

Beauchard, K., and M. Mirrahimi. "Approximate stabilization of a quantum particle in a 1D infinite potential well." IFAC Proceedings Volumes 41, no. 2 (2008): 8737–42. http://dx.doi.org/10.3182/20080706-5-kr-1001.01477.

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8

Harris, Richard, Jacobus Terblans, and Hendrik Swart. "Exciton binding energy in an infinite potential semiconductor quantum well–wire heterostructure." Superlattices and Microstructures 86 (October 2015): 456–66. http://dx.doi.org/10.1016/j.spmi.2015.08.010.

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9

Mousavi, S. V. "Quantum effective force in an expanding infinite square-well potential and Bohmian perspective." Physica Scripta 86, no. 3 (August 24, 2012): 035004. http://dx.doi.org/10.1088/0031-8949/86/03/035004.

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10

Kilbane, D., A. Cummings, G. O’Sullivan, and D. M. Heffernan. "The classical-quantum correspondence of a kicked particle in an infinite potential well." Chaos, Solitons & Fractals 30, no. 2 (October 2006): 424–40. http://dx.doi.org/10.1016/j.chaos.2006.01.011.

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11

GARCÍA, MARCOS A. G., and ALEXANDER V. TURBINER. "THE QUANTUM H3 INTEGRABLE SYSTEM." International Journal of Modern Physics A 25, no. 30 (December 10, 2010): 5567–94. http://dx.doi.org/10.1142/s0217751x10050597.

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The quantum H3 integrable system is a three-dimensional system with rational potential related to the noncrystallographic root system H3. It is shown that the gauge-rotated H3 Hamiltonian as well as one of the integrals, when written in terms of the invariants of the Coxeter group H3, is in algebraic form: it has polynomial coefficients in front of derivatives. The Hamiltonian has infinitely-many finite-dimensional invariant subspaces in polynomials, they form the infinite flag with the characteristic vector [Formula: see text]. One among possible integrals is found (of the second order) as well as its algebraic form. A hidden algebra of the H3 Hamiltonian is determined. It is an infinite-dimensional, finitely-generated algebra of differential operators possessing finite-dimensional representations characterized by a generalized Gauss decomposition property. A quasi-exactly-solvable integrable generalization of the model is obtained. A discrete integrable model on the uniform lattice in a space of H3-invariants "polynomially"-isospectral to the quantum H3 model is defined.

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12

Lee, S. H., J. Y. Choi, J. H. Park, J. Y. Sug, S. T. Bae, and J. G. Kim. "The Quantum Optical Transition Properties of ZnO in an Infinite Square Well Potential System." Journal of the Korean Physical Society 54, no. 6 (June 15, 2009): 2212–18. http://dx.doi.org/10.3938/jkps.54.2212.

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13

Beauchard, Karine, and Mazyar Mirrahimi. "Practical Stabilization of a Quantum Particle in a One-Dimensional Infinite Square Potential Well." SIAM Journal on Control and Optimization 48, no. 2 (January 2009): 1179–205. http://dx.doi.org/10.1137/070704204.

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14

Thang, Nguyen Quyet, Nguyen Van Nghia, and Nguyen Quang Bau. "The Influence of Electromagnetic Wave on the Acoustomagnetoelectric Effect in a Quantum Well with Infinite Potential." Key Engineering Materials 789 (November 2018): 6–13. http://dx.doi.org/10.4028/www.scientific.net/kem.789.6.

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The influence of electromagnetic wave (EMW) on the acous- tomagnetoelectric (AME)effect is studied theoretically in a quantum well. The expression of the AME field is obtained. Thedependences of the AME field on the temperature of system, the frequency of acoustic wave, thefrequency and intensity of electromagnetic wave and the parameters of a Quantum well are nonlinear.These dependences in the case of QW are different and more complex than in the case of bulksemiconductor. The results are numerically calculated and discussed for an GaAs/AGaAs QW. Thegraph of the dependence of the AME field on the frequency of acoustic wave shows that the changesof external magnetic field drag on the change of value of AME field and the change of the positionof AME field. The value of the AME field in case with the intensity of EMW is much bigger than incase without the intensity of EMW.

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15

Tita, Amornthep, and Pichet Vanichchapongjaroen. "Bound states of Newton’s equivalent finite square well." Modern Physics Letters A 33, no. 33 (October 29, 2018): 1850195. http://dx.doi.org/10.1142/s021773231850195x.

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In this paper, a one-parameter family of Newton’s equivalent Hamiltonians (NEH) for finite square well potential is analyzed in order to obtain bound state energy spectrum and wave functions. For a generic potential, each of the NEH is classically equivalent to one another and to the standard Hamiltonian yielding Newton’s equations. Quantum mechanically, however, they are expected to be different from each other. The Schrödinger’s equation coming from each NEH with finite square well potential is an infinite order differential equation. The matching conditions, therefore, demand the wave functions to be infinitely differentiable at the well boundaries. To handle this, we provide a way to consistently truncate these conditions. It turns out as expected that bound state energy spectrum and wave functions are dependent on the parameter [Formula: see text] which is used to characterize different NEH. As [Formula: see text], the energy spectrum coincides with that from the standard quantum finite square well.

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16

GARCÍA, MARCOS A. G., and ALEXANDER V. TURBINER. "THE QUANTUM H4 INTEGRABLE SYSTEM." Modern Physics Letters A 26, no. 06 (February 28, 2011): 433–47. http://dx.doi.org/10.1142/s0217732311034839.

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The quantum H4 integrable system is a 4D system with rational potential related to the non-crystallographic root system H4 with 600-cell symmetry. It is shown that the gauge-rotated H4 Hamiltonian as well as one of the integrals, when written in terms of the invariants of the Coxeter group H4, is in algebraic form: it has polynomial coefficients in front of the derivatives. Any eigenfunction is a polynomial multiplied by ground-state function (factorization property). Spectra correspond to one of the anisotropic harmonic oscillators. The Hamiltonian has infinitely-many finite-dimensional invariant subspaces in polynomials, they form the infinite flag with the characteristic vector α = (1, 5, 8, 12).

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17

ZOLI, MARCO. "INSTANTON SOLUTION OF A NONLINEAR POTENTIAL IN FINITE SIZE." International Journal of Modern Physics B 22, no. 04 (February 10, 2008): 327–42. http://dx.doi.org/10.1142/s021797920803865x.

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The Euclidean path integral method is applied to a quantum tunneling model which accounts for finite size (L) effects. The general solution of the Euler Lagrange equation for the double well potential is found in terms of Jacobi elliptic functions. The antiperiodic instanton interpolates between the potential minima at any finite L inside the quantum regime, and generalizes the well-known (anti)kink solution of the infinite size case. The derivation of the functional determinant, stemming from the quantum fluctuation contribution, is given in detail. The explicit formula for the finite size semiclassical path integral is presented.

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18

COHEN, AVRAHAM, and SHMUEL FISHMAN. "CLASSICAL DIFFUSION AND QUANTAL LOCALIZATION OF A KICKED PARTICLE IN A WELL." International Journal of Modern Physics B 02, no. 01 (February 1988): 103–20. http://dx.doi.org/10.1142/s0217979288000093.

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The classical and quantal behavior of a particle in an infinite potential well, that is periodically kicked is studied. The kicking potential is K|q|α, where q is the coordinate, while K and α are constants. Classically, it is found that for α > 2 the energy of the particle increases diffusively, for α < 2 it is bounded and for α = 2 the result depends on K. An approximate formula for the diffusion coefficient is presented and compared with numerical results. For quantum systems that are chaotic in the classical limit, diffusive growth of energy takes place for a short time and then it is suppressed by quantal effects. For the systems that are studied in this work the origin of the quantal localization in energy is related to the one of classical chaos.

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19

Lee, Johnson, and M. O. Vassell. "Influence of uniaxial stress on hole effective masses in quantum wells." Canadian Journal of Physics 66, no. 12 (December 1, 1988): 1088–93. http://dx.doi.org/10.1139/p88-174.

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The hole effective masses in quantum wells under uniaxial stress are investigated. The valence subband structures are determined from a 4 × 4 Luttinger–Kohn Hamiltonian together with a 4 × 4 strain Hamiltonian with appropriate boundary conditions. The variations of the hole effective masses with well width, stress, and potential-barrier height (or the corresponding alloy composition) are discussed and found to be drastic. For example, even if the quantum well is stress free, the variations of the hole effective masses with well width can range from +∞ to −∞ and are not constant, as predicted by the infinite potential-well model. The variations with stress indicate that the effective masses can become zero, depending on the direction and the magnitude of the stress.

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20

YANCEY, AMBER N., SEONG-GON KIM, and JOHN T. FOLEY. "VISUALIZING COMPLICATED QUANTUM MECHANICAL BEHAVIOR FROM SIMPLE 2D POTENTIALS USING WEBTOP." International Journal of Modern Physics C 20, no. 09 (September 2009): 1431–41. http://dx.doi.org/10.1142/s0129183109014497.

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The ability to simulate several aspects of two-dimensional quantum mechanics is discussed, in conjunction with an ongoing visualization project, WebTOP, that has been of recognizable importance to physics education since its inception in the late 1990s. In the past, the WebTOP project has been primarily used as a means of visualizing optics and wave phenomena and, now, the development of certain interactive quantum mechanical demonstrations has the potential to strengthen its power as an educational tool for the physics community. The added functionality for propagating wave packets forward in time for a given 2D potential gives rise to the ability to investigate interesting quantum behaviors. Fractional revivals of states in the 2D infinite square well can be clearly seen as well as the time delay of scattered wave packets for certain step potentials. Aspects of squeezed and coherent states of the 2D harmonic oscillator potential can also be explored, among other observable phenomena.

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21

Flom, Ofir, Asher Yahalom, Haggai Zilberberg, L. P. Horwitz, and Jacob Levitan. "Quantum complexity associated with tunneling." Quantum Information and Computation 19, no. 3&4 (March 2019): 222–36. http://dx.doi.org/10.26421/qic19.3-4-3.

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We use a one dimensional model of a square barrier embedded in an infinite potential well to demonstrate that tunneling leads to a complex behavior of the wave function and that the degree of complexity may be quantified by use of a locally defined spatial entropy function defined by S=-\int |\Psi(x,t)|^2 \ln |\Psi(x,t)|^2 dx . We show that changing the square barrier by increasing the height or width of the barrier not only decreases the tunneling but also slows down the rapid rise of the entropy function, indicating that the locally defined entropy growth is an essentially quantum effect.

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22

Aguilar, L. M. Arévalo, F. Velasco Luna, C. Robledo-Sánchez, and M. L. Arroyo-Carrasco. "The infinite square well potential and the evolution operator method for the purpose of overcoming misconceptions in quantum mechanics." European Journal of Physics 35, no. 2 (January 17, 2014): 025001. http://dx.doi.org/10.1088/0143-0807/35/2/025001.

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23

Sharma, Aditi, and O. S. K. S. Sastri. "Numerical simulation of quantum anharmonic oscillator, embedded within an infinite square well potential, by matrix methods using Gnumeric spreadsheet." European Journal of Physics 41, no. 5 (August 13, 2020): 055402. http://dx.doi.org/10.1088/1361-6404/ab988c.

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24

Coron, Jean-Michel. "On the small-time local controllability of a quantum particle in a moving one-dimensional infinite square potential well." Comptes Rendus Mathematique 342, no. 2 (January 2006): 103–8. http://dx.doi.org/10.1016/j.crma.2005.11.004.

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25

ZOU, JIAN, and BIN SHAO. "QUANTUM EFFECTS OF A PARTICLE IN AN INFINITE SQUARE WELL WITH A MOVING WALL." International Journal of Modern Physics B 14, no. 10 (April 20, 2000): 1059–65. http://dx.doi.org/10.1142/s0217979200001308.

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The quantum behavior of a particle in a one-dimensional infinite square well potential with a moving wall is studied. The particle is assumed to be initially prepared in the coherent state (Gaussian wave packet) and although the boundary is far from the particle, it is shown that the changing of the boundary conditions can instantaneously affect the dynamical behavior of the particle. It is also shown that the initial state can evolve into a squeezed state, and in some cases the spreading of the wavepacket could be suppressed. Finally the Pancharatnam phase is also discussed.

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26

Chung, Won Sang, and Hassan Hassanabadi. "Fermi energy in the q-deformed quantum mechanics." Modern Physics Letters A 35, no. 11 (January 17, 2020): 2050074. http://dx.doi.org/10.1142/s0217732320500741.

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In this paper, we use the q-derivative emerging in the non-extensive statistical physics to formulate the q-deformed quantum mechanics. We find the algebraic structure related to this deformed theory and investigate some properties of the q-deformed elementary functions. Using this mathematical background, we formulate the q-deformed Heisenberg algebra and q-deformed time-dependent Schrödinger equation. As an example, we deal with the infinite potential well and compute the Fermi energy in the q-deformed theory.

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27

ÇAKIR, BEKİR, AYHAN ÖZMEN, ÜLFET ATAV, HÜSEYİN YÜKSEL, and YUSUF YAKAR. "CALCULATION OF ELECTRONIC STRUCTURE OF A SPHERICAL QUANTUM DOT USING A COMBINATION OF QUANTUM GENETIC ALGORITHM AND HARTREE–FOCK–ROOTHAAN METHOD." International Journal of Modern Physics C 19, no. 04 (April 2008): 599–609. http://dx.doi.org/10.1142/s0129183108012315.

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The electronic structure of Quantum Dot (QD), GaAs/Al x Ga 1-x As , has been investigated by using a combination of Quantum Genetic Algorithm (QGA) and Hartree–Fock–Roothaan (HFR) method. One-electron system with an on-center impurity is considered by assuming a spherically symmetric confining potential of finite depth. The ground and excited state energies of one-electron QD were calculated depending on the dot radius and stoichiometric ratio. Expectation values of energy were determined by using the HFR method along with Slater-Type Orbitals (STOs) and QGA was used for the wavefunctions optimization. In addition, the effect of the size of the basis set on the energy of QD was investigated. We also calculated the binding energy for a dot with finite confining potential. We found that the impurity binding energy increases for the finite potential well when the dot radius decreases. For the finite potential well, the binding energy reaches a peak value and then diminishes to a limiting value corresponding to the radius for which there are no bound states in the well. Whereas in previous study, in Ref. 40, for the infinite potential well, we found that the impurity binding energy increases as the dot radius decreases.

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28

Chattopadhyay, Pritam, Ayan Mitra, Goutam Paul, and Vasilios Zarikas. "Bound on Efficiency of Heat Engine from Uncertainty Relation Viewpoint." Entropy 23, no. 4 (April 9, 2021): 439. http://dx.doi.org/10.3390/e23040439.

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Quantum cycles in established heat engines can be modeled with various quantum systems as working substances. For example, a heat engine can be modeled with an infinite potential well as the working substance to determine the efficiency and work done. However, in this method, the relationship between the quantum observables and the physically measurable parameters—i.e., the efficiency and work done—is not well understood from the quantum mechanics approach. A detailed analysis is needed to link the thermodynamic variables (on which the efficiency and work done depends) with the uncertainty principle for better understanding. Here, we present the connection of the sum uncertainty relation of position and momentum operators with thermodynamic variables in the quantum heat engine model. We are able to determine the upper and lower bounds on the efficiency of the heat engine through the uncertainty relation.

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29

BORGES, ANTÔNIO NEWTON, FRANCISCO A. P. OSÓRIO, PAULO CÉSAR MIRANDA MACHADO, and OSCAR HIPÓLITO. "SHORT-RANGE CORRELATION EFFECTS IN A POLARON GAS IN GaAs–AlGaAs QUANTUM WELL WIRES." Modern Physics Letters B 13, no. 22n23 (October 10, 1999): 819–27. http://dx.doi.org/10.1142/s0217984999001019.

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We investigate the short-range correlation effects of plasmon–phonon collective excitations in a quantum well wire by using the self-consistent field approximation theory proposed by Singwi, Tosi, Land and Sjolander [Phys. Rev.176, 589 (1968)]. In our calculation model, we consider a three-subband model with only one populated, for a rectangular cross-section quantum well wire with infinite height for the potential barrier. We have verified that by decreasing the wire width (and/or decreasing the electronic density), the local field correction effects are increased. We compare the present results with those obtained within the Random Phase Approximation throughout the paper and found that the differences between the two calculation methods are more significant for the intrasubband plasmon.

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30

Ivlev, Boris I. "On formation of long-living states." Canadian Journal of Physics 94, no. 12 (December 2016): 1253–58. http://dx.doi.org/10.1139/cjp-2016-0227.

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The motion of a particle in a potential well is studied when the particle is attached to an infinite elastic string. This is generic with the problem of dissipative quantum mechanics investigated by Caldeira and Leggett (Ann. Phys. 149, 374 (1983). doi: 10.1016/0003-4916(83)90202-6 ). Besides the dissipative motion there is another scenario of interaction of the string with the particle attached. Stationary particle–string states exist with string deformations accompanying the particle. This is like polaronic states in solids. Our polaronic states in the well are non-decaying and have a continuous energy spectrum. These states may have a link to quantum electrodynamics.

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31

Harry, S. T., and M. A. Adekanmbi. "CONFINEMENT ENERGY OF QUANTUM DOTS AND THE BRUS EQUATION." International Journal of Research -GRANTHAALAYAH 8, no. 11 (December 16, 2020): 318–23. http://dx.doi.org/10.29121/granthaalayah.v8.i11.2020.2451.

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A review of the ground state confinement energy term in the Brus equation for the bandgap energy of a spherically shaped semiconductor quantum dot was made within the framework of effective mass approximation. The Schrodinger wave equation for a spherical nanoparticle in an infinite spherical potential well was solved in spherical polar coordinate system. Physical reasons in contrast to mathematical expediency were considered and solution obtained. The result reveals that the shift in the confinement energy is less than that predicted by the Brus equation as was adopted in most literatures.

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32

Bilynskyi, I. V., R. Ya Leshko, H. O. Metsan, and I. S. Shevchuk. "Hole States in Spherical Quantum Nanoheterosystem with Intermediate Spin-Orbital Interaction." Фізика і хімія твердого тіла 20, no. 3 (October 18, 2019): 227–33. http://dx.doi.org/10.15330/pcss.20.3.227-233.

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The hole energy spectrum has been studied for the spherical semiconductor nanoheterosystem with the cubic symmetry. The exact solutions of the Schrödinger equation for the ground and excited hole states are presented within the framework of the 6-band Luttinger Hamiltonian and the finite gap of bands with the corresponding boundary conditions. Dependence of the holes energies from the radius of the quantum dot has been calculated for the GaAs/AlAs heterostructure. Obtained results where compared with data obtained using the infinite potential well model, as well as the single-band model for heavy and light holes.

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33

REGO-MONTEIRO, M. A., and E. M. F. CURADO. "CONSTRUCTION OF A NON-STANDARD QUANTUM FIELD THEORY USING GENERALIZED HEISENBERG ALGEBRA." International Journal of Modern Physics A 17, no. 05 (February 20, 2002): 661–73. http://dx.doi.org/10.1142/s0217751x0200959x.

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We herein construct a Heisenberg-like algebra for the one-dimensional quantum free Klein–Gordon equation defined on the interval of the real line of length L. Using the realization of the ladder operators of this Heisenberg-type algebra in terms of physical operators we build a (3+1)-dimensional free quantum field theory based on this algebra. We introduce fields written in terms of the ladder operators of this Heisenberg-type algebra and a free quantum Hamiltonian in terms of these fields. The mass spectrum of the physical excitations of this quantum field theory is given by [Formula: see text], where n=1,2,… and mq is the mass of a particle in a relativistic infinite square-well potential of width L.

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34

Reyes, J. C. Salcedo. "Kinematic Study of Refraction Properties of a ZnSe-ZnTe Dielectric Grating." Journal of Nanoscience and Nanotechnology 8, no. 12 (December 1, 2008): 6589–92. http://dx.doi.org/10.1166/jnn.2008.18430.

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The plane wave expansion method is applied to determine the thickness of the ZnSe-ZnTe slabs in a semi-infinite dielectric grating in such a way that the maximum reflectivity of the system is obtained. In this way the potential of the ZnSe-ZnTe system for applications in CdSe ultra thin quantum well based monolithic II–VI Vertical Cavity Surface Emitting Laser for the green spectral region is demonstrated. A kinematic analysis of the thickness-dependent refraction at the boundary between a ZnSe-ZnTe semi-infinite one dimensional photonic crystal and a homogeneous material in transverse magnetic polarization and oblique incidence case is presented.

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35

Granovskyi, Ya I., M. M. Malamud, and H. Neidhardt. "Quantum graphs with summable matrix potentials." Доклады Академии наук 488, no. 1 (September 24, 2019): 5–10. http://dx.doi.org/10.31857/s0869-565248815-10.

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Let G be a metric, finite, noncompact, and connected graph with finitely many edges and vertices. Assume also that the length at least of one of the edges is infinite. The main object of the paper is Hamiltonian Hα associated in L2(G; Cm) with matrix Sturm-Liouville’s expression and boundary delta-type conditions at each vertex. Assuming that the potential matrix is summable and applying technique of boundary triplets and the corresponding Weyl functions we show that the singular continuous spectrum of the Hamiltonian Hα as well as any other self-adjoint realization of the Sturm-Liouville expression is empty. We also indicate conditions on the graph ensuring the positive part of the Hamiltonian Hα to be purely absolutely continuous. Under an additional condition on the potential matrix the Bargmann type estimate for the number of the negative eigenvalues of the operator Hα is obtained. Also we find a formula for the scattering matrix of the pair {Hα, HD} where HD is the operator of the Dirichlet problem on the graph.

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36

Badalov, V. H., B. Baris, and K. Uzun. "Bound states of the D-dimensional Schrödinger equation for the generalized Woods–Saxon potential." Modern Physics Letters A 34, no. 14 (May 10, 2019): 1950107. http://dx.doi.org/10.1142/s0217732319501074.

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The formal framework for quantum mechanics is an infinite number of dimensional space. Hereby, in any analytical calculation of the quantum system, the energy eigenvalues and corresponding wave functions can be represented easily in a finite-dimensional basis set. In this work, the approximate analytical solutions of the hyper-radial Schrödinger equation are obtained for the generalized Wood–Saxon potential by implementing the Pekeris approximation to surmount the centrifugal term. The energy eigenvalues and corresponding hyper-radial wave functions are derived for any angular momentum case by means of state-of-the-art Nikiforov–Uvarov and supersymmetric quantum mechanics methods. Hence, the same expressions are obtained for the energy eigenvalues, and the expression of hyper-radial wave functions transforming each other is shown owing to these methods. Furthermore, a finite number energy spectrum depending on the depths of the potential well [Formula: see text] and [Formula: see text], the radial [Formula: see text] and [Formula: see text] orbital quantum numbers and parameters [Formula: see text], [Formula: see text], [Formula: see text] are also identified in detail. Next, the bound state energies and corresponding normalized hyper-radial wave functions for the neutron system of the [Formula: see text]Fe nucleus are calculated in [Formula: see text] and [Formula: see text] as well as the energy spectrum expressions of other higher dimensions are revealed by using the energy spectrum of [Formula: see text] and [Formula: see text].

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37

Levinsen, Jesper, Pietro Massignan, Georg M. Bruun, and Meera M. Parish. "Strong-coupling ansatz for the one-dimensional Fermi gas in a harmonic potential." Science Advances 1, no. 6 (July 2015): e1500197. http://dx.doi.org/10.1126/sciadv.1500197.

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A major challenge in modern physics is to accurately describe strongly interacting quantum many-body systems. One-dimensional systems provide fundamental insights because they are often amenable to exact methods. However, no exact solution is known for the experimentally relevant case of external confinement. We propose a powerful ansatz for the one-dimensional Fermi gas in a harmonic potential near the limit of infinite short-range repulsion. For the case of a single impurity in a Fermi sea, we show that our ansatz is indistinguishable from numerically exact results in both the few- and many-body limits. We furthermore derive an effective Heisenberg spin-chain model corresponding to our ansatz, valid for any spin-mixture, within which we obtain the impurity eigenstates analytically. In particular, the classical Pascal’s triangle emerges in the expression for the ground-state wave function. As well as providing an important benchmark for strongly correlated physics, our results are relevant for emerging quantum technologies, where a precise knowledge of one-dimensional quantum states is paramount.

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38

Oketch, F., and H. Oyoko. "A theoretical study of variation of photoionization cross section of donor impurities in a GaAs quantum dot of cylindrical geometry with incident photon frequency, donor location along the dot axis and applied uniaxial stress." Revista Mexicana de Física 66, no. 1 (December 28, 2019): 35. http://dx.doi.org/10.31349/revmexfis.66.35.

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In this work, we have used a variational technique within the effective mass approximation to study the variation of the photoionization cross section of a donor impurity in a cylindrical GaAs quantum dot with incident photon frequencies and applied uniaxial stress. We have used the dipole approximation and assumed that the barrier potential is infinite. Our results show that the photoionization cross section begins at a finite value and increases with increasing frequency until it reaches a peak and then it decreases gradually, almost exponentially, until it reaches a finite value when it is almost insensitive to any further increase in frequency. Furthermore, for a particular quantum dot length, the photoionization cross section decreases with increasing applied uniaxial stress. We have also noted that the longer the quantum well dot the larger is the photoionization cross section

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39

PETER, A. JOHN. "THE EFFECT OF POSITION DEPENDENT EFFECTIVE MASS OF HYDROGENIC IMPURITIES IN PARABOLIC GaAs/GaAlAs QUANTUM DOTS IN A STRONG MAGNETIC FIELD." International Journal of Modern Physics B 23, no. 26 (October 20, 2009): 5109–18. http://dx.doi.org/10.1142/s0217979209053394.

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The binding energy of shallow hydrogenic impurities in parabolic GaAs/GaAlAs quantum dots is calculated as a function of dot radius in the influence of magnetic field. The binding energy has been calculated following a variational procedure within the effective-mass approximation. Calculations are presented with constant effective-mass and position dependent effective masses. A finite confining potential well with depth is determined by the discontinuity of the band gap in the quantum dot and the cladding. The results show that the impurity binding energy (i) increases as the dot radius decreases for the infinite case, (ii) reaches a peak value around 1R* as the dot radius decreases and then diminishes to a limiting value corresponding to the radius for which there are no bound states in the well for the infinite case, and (iii) increases with the magnetic field. Also it is found that (i) the use of constant effective mass (0.067 m0) is justified for dot sizes ≥ a* where a* is the effective Bohr radius which is about 100 Å for GaAs , in the estimation of ionization energy and (ii) the binding energy shows complicated behavior when the position dependent mass is included for the dot size ≤ a*. These results are compared with the available existing literatures.

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40

Ngoc, Hoang Van. "The dependence of the conductivity tensor on electromagnetic waves and laser fields in a quantum well with infinite potential in the case of electrons - optical phonon scattering." IOP Conference Series: Materials Science and Engineering 1070, no. 1 (February 1, 2021): 012077. http://dx.doi.org/10.1088/1757-899x/1070/1/012077.

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41

Mashford, John. "Divergence-free quantum electrodynamics in locally conformally flat space–time." International Journal of Modern Physics A 36, no. 13 (May 6, 2021): 2150083. http://dx.doi.org/10.1142/s0217751x21500834.

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This paper describes an approach to quantum electrodynamics (QED) in curved space–time obtained by considering infinite-dimensional algebra bundles associated to a natural principal bundle [Formula: see text] associated with any locally conformally flat space–time, with typical fibers including the Fock space and a space of fermionic multiparticle states which forms a Grassmann algebra. Both these algebras are direct sums of generalized Hilbert spaces. The requirement of [Formula: see text] covariance associated with the geometry of space–time, where [Formula: see text] is the structure group of [Formula: see text], leads to the consideration of [Formula: see text] intertwining operators between various spaces. Scattering processes are associated with such operators and are encoded in an algebra of kernels. Intertwining kernels can be generated using [Formula: see text] covariant matrix-valued measures. Feynman propagators, fermion loops and the electron self-energy can be given well-defined interpretations as such measures. Divergence-free calculations in QED can be carried out by computing the spectra of these measures and kernels (a process called spectral regularization). As an example of the approach the precise Uehling potential function for the [Formula: see text] atom is calculated without requiring renormalization from which the Uehling contribution to the Lamb shift can be calculated exactly.

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42

Rahayu, Prapti, and Witri Wahyu Lestari. "STUDY OF SYNTHESIS AND CHARACTERIZATION OF METAL-ORGANIC FRAMEWORKS MOF-5 AS HYDROGEN STORAGE MATERIAL." ALCHEMY Jurnal Penelitian Kimia 12, no. 1 (August 17, 2016): 14. http://dx.doi.org/10.20961/alchemy.12.1.934.14-26.

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<p>Metal-organic frameworks (MOFs) are porous coordination polymer containing bi-or polidentate organic linker coordinated with inorganic part, such as metal oxide cluster or metal cation as node which called as secondary building unit (SBU) to form infinite structure. Due to high porosity and surface area, good thermal stability as well as the availability of unsaturated metal center or the linker influence attracts the interaction with gases, thus MOFs have potential to be applied as hydrogen storage material. One type of MOFs that have been widely studied is [Zn<sub>4</sub>O(benzene-1,4-dicarboxylate)<sub>3</sub>], namely, MOF-5.Various synthesis method have been developed to obtain optimum results. Characterization of MOF-5 from various synthesis method such as crystallinity, capacity, stability, and quantum dot behavior of MOF-5 have been summarized in this review.</p>

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43

Rahayu, Prapti, and Witri Wahyu Lestari. "STUDY OF SYNTHESIS AND CHARACTERIZATION OF METAL-ORGANIC FRAMEWORKS MOF-5 AS HYDROGEN STORAGE MATERIAL." ALCHEMY Jurnal Penelitian Kimia 12, no. 1 (August 17, 2016): 14. http://dx.doi.org/10.20961/alchemy.v12i1.934.

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<p>Metal-organic frameworks (MOFs) are porous coordination polymer containing bi-or polidentate organic linker coordinated with inorganic part, such as metal oxide cluster or metal cation as node which called as secondary building unit (SBU) to form infinite structure. Due to high porosity and surface area, good thermal stability as well as the availability of unsaturated metal center or the linker influence attracts the interaction with gases, thus MOFs have potential to be applied as hydrogen storage material. One type of MOFs that have been widely studied is [Zn<sub>4</sub>O(benzene-1,4-dicarboxylate)<sub>3</sub>], namely, MOF-5.Various synthesis method have been developed to obtain optimum results. Characterization of MOF-5 from various synthesis method such as crystallinity, capacity, stability, and quantum dot behavior of MOF-5 have been summarized in this review.</p>

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44

Olendski, Oleg. "Rényi and Tsallis Entropies of the Aharonov–Bohm Ring in Uniform Magnetic Fields." Entropy 21, no. 11 (October 29, 2019): 1060. http://dx.doi.org/10.3390/e21111060.

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One-parameter functionals of the Rényi R ρ , γ ( α ) and Tsallis T ρ , γ ( α ) types are calculated both in the position (subscript ρ ) and momentum ( γ ) spaces for the azimuthally symmetric 2D nanoring that is placed into the combination of the transverse uniform magnetic field B and the Aharonov–Bohm (AB) flux ϕ A B and whose potential profile is modeled by the superposition of the quadratic and inverse quadratic dependencies on the radius r. Position (momentum) Rényi entropy depends on the field B as a negative (positive) logarithm of ω e f f ≡ ω 0 2 + ω c 2 / 4 1 / 2 , where ω 0 determines the quadratic steepness of the confining potential and ω c is a cyclotron frequency. This makes the sum R ρ n m ( α ) + R γ n m ( α 2 α − 1 ) a field-independent quantity that increases with the principal n and azimuthal m quantum numbers and satisfies the corresponding uncertainty relation. In the limit α → 1 , both entropies in either space tend to their Shannon counterparts along, however, different paths. Analytic expression for the lower boundary of the semi-infinite range of the dimensionless coefficient α where the momentum entropies exist reveals that it depends on the ring geometry, AB intensity, and quantum number m. It is proved that there is the only orbital for which both Rényi and Tsallis uncertainty relations turn into the identity at α = 1 / 2 , which is not necessarily the lowest-energy level. At any coefficient α , the dependence of the position of the Rényi entropy on the AB flux mimics the energy variation with ϕ A B , which, under appropriate scaling, can be used for the unique determination of the associated persistent current. Similarities and differences between the two entropies and their uncertainty relations are discussed as well.

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UGULAVA, A., L. CHOTORLISHVILI, K. NICKOLADZE, and G. MCHEDLISHVILI. "CHAOTIC PHENOMENON IN NONLINEAR GYROTROPIC MEDIUM." International Journal of Modern Physics B 22, no. 04 (February 10, 2008): 381–405. http://dx.doi.org/10.1142/s0217979208038570.

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Nonlinear gyrotropic medium is a medium whose natural optical activity depends on the intensity of the incident light wave. The Kuhn's model is used to study nonlinear gyrotropic medium with great success. The Kuhn's model presents itself as a model of nonlinear coupled oscillators. In the study of the Kuhn's nonlinear model, classical dynamics in the case of weak as well as strong nonlinearity is analysed. In the case of weak nonlinearity, analytical solutions which are in good agreement with the numerical solutions are obtained. In the case of strong nonlinearity, the values of those parameters for which chaos is formed in the system under study have been determined. The subject of interest is also the question of the Kuhn's model integrability. It is seen that at certain values of the interaction potential, this model is exactly integrable and under certain conditions, it is reduced to the so-called universal Hamiltonian. In the case of quantum-mechanical consideration, the possibility of stochastic absorption of external field energy by nonlinear gyrotropic medium is shown. Finally, further generalization of the Kuhn's model for an infinite chain of interacting oscillators is offered.

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Towler, M. D., N. J. Russell, and Antony Valentini. "Time scales for dynamical relaxation to the Born rule." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2140 (November 30, 2011): 990–1013. http://dx.doi.org/10.1098/rspa.2011.0598.

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We illustrate through explicit numerical calculations how the Born rule probability densities of non-relativistic quantum mechanics emerge naturally from the particle dynamics of de Broglie–Bohm pilot-wave theory. The time evolution of a particle distribution initially not equal to the absolute square of the wave function is calculated for a particle in a two-dimensional infinite potential square well. Under the de Broglie–Bohm ontology, the box contains an objectively existing ‘pilot wave’ which guides the electron trajectory, and this is represented mathematically by a Schrödinger wave function composed of a finite out-of-phase superposition of M energy eigenstates (with M ranging from 4 to 64). The electron density distributions are found to evolve naturally into the Born rule ones and stay there; in analogy with the classical case this represents a decay to ‘quantum equilibrium’. The proximity to equilibrium is characterized by the coarse-grained subquantum H -function which is found to decrease roughly exponentially towards zero over the course of time. The time scale τ for this relaxation is calculated for various values of M and the coarse-graining length ε . Its dependence on M is found to disagree with an earlier theoretical prediction. A power law, τ ∝ M −1 , is found to be fairly robust for all coarse-graining lengths and, although a weak dependence of τ on ε is observed, it does not appear to follow any straightforward scaling. A theoretical analysis is presented to explain these results. This improvement in our understanding of time scales for relaxation to quantum equilibrium is likely to be of use in the development of models of relaxation in the early Universe, with a view to constraining possible violations of the Born rule in inflationary cosmology.

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Linetsky, Vadim. "The spectral representation of Bessel processes with constant drift: applications in queueing and finance." Journal of Applied Probability 41, no. 02 (June 2004): 327–44. http://dx.doi.org/10.1017/s0021900200014339.

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Bessel processes with constant negative drift have recently appeared as heavy-traffic limits in queueing theory. We derive a closed-form expression for the spectral representation of the transition density of the Bessel process of orderν> −1 with constant driftμ≠ 0. Whenν> -½ andμ< 0, the first term of the spectral expansion is the steady-state gamma density corresponding to the zero principal eigenvalueλ0= 0, followed by an infinite series of terms corresponding to the higher eigenvaluesλn,n= 1,2,…, as well as an integral over the continuous spectrum aboveμ2/2. When −1 <ν< -½ andμ< 0, there is only one eigenvalueλ0= 0 in addition to the continuous spectrum. As well as applications in queueing, Bessel processes with constant negative drift naturally lead to two new nonaffine analytically tractable specifications for short-term interest rates, credit spreads, and stochastic volatility in finance. The two processes serve as alternatives to the CIR process for modelling mean-reverting positive economic variables and have nonlinear infinitesimal drift and variance. On a historical note, the Sturm–Liouville equation associated with Bessel processes with constant negative drift is closely related to the celebrated Schrödinger equation with Coulomb potential used to describe the hydrogen atom in quantum mechanics. Another connection is with D. G. Kendall's pole-seeking Brownian motion.

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48

REINISCH, G. "NONLINEAR KLEIN-GORDON SOLITON MECHANICS." International Journal of Modern Physics B 06, no. 21 (November 10, 1992): 3395–440. http://dx.doi.org/10.1142/s021797929200150x.

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Nonlinear Klein-Gordon solitary waves — or “solitons” in a loose sense — in n+1 dimensions, driven by very general external fields which must only satisfy continuity — together with regularity conditions at the boundaries of the system, obey a quite simple equation of motion. This equation is the exact generalization to this dynamical system of infinite number of degrees of freedom — which may be conservative or not — of the second Newton’s law setting the basis of material point mechanics. In the restricted case of conservative nonlinear Klein-Gordon systems, where the external driving force is derivable from a potential energy, we recover the generalized Ehrenfest theorem which was itself the extension to such systems of the well-known Ehrenfest theorem in quantum mechanics (G. Reinisch and J.C. Fernandez, Phys. Rev. Lett.67, 1968 (1991)). This review paper first displays a few (of one-dimensional sine-Gordon type) typical examples of the basic difficulties related to the trial construction of solitary-wave mechanics. Then the general equation of motion of nonlinear Klein-Gordon solitary waves is proved and the derivation of the previous sine-Gordon examples from this theorem is displayed. Two-dimensional nonlinear solitary-wave patterns are considered, as well as a special emphasis is put on the applications to space-time complexity of 1-dim. sine-Gordon systems.

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49

Linetsky, Vadim. "The spectral representation of Bessel processes with constant drift: applications in queueing and finance." Journal of Applied Probability 41, no. 2 (June 2004): 327–44. http://dx.doi.org/10.1239/jap/1082999069.

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Bessel processes with constant negative drift have recently appeared as heavy-traffic limits in queueing theory. We derive a closed-form expression for the spectral representation of the transition density of the Bessel process of order ν > −1 with constant drift μ ≠ 0. When ν > -½ and μ < 0, the first term of the spectral expansion is the steady-state gamma density corresponding to the zero principal eigenvalue λ0 = 0, followed by an infinite series of terms corresponding to the higher eigenvalues λn, n = 1,2,…, as well as an integral over the continuous spectrum above μ2/2. When −1 < ν < -½ and μ < 0, there is only one eigenvalue λ0 = 0 in addition to the continuous spectrum. As well as applications in queueing, Bessel processes with constant negative drift naturally lead to two new nonaffine analytically tractable specifications for short-term interest rates, credit spreads, and stochastic volatility in finance. The two processes serve as alternatives to the CIR process for modelling mean-reverting positive economic variables and have nonlinear infinitesimal drift and variance. On a historical note, the Sturm–Liouville equation associated with Bessel processes with constant negative drift is closely related to the celebrated Schrödinger equation with Coulomb potential used to describe the hydrogen atom in quantum mechanics. Another connection is with D. G. Kendall's pole-seeking Brownian motion.

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50

Isojärvi, T. "Quantum mechanics of particles trapped in a Lamé circle or Lamé sphere shaped potential well." Revista Mexicana de Física 67, no. 2 Mar-Apr (July 15, 2021): 206–18. http://dx.doi.org/10.31349/revmexfis.67.206.

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Ground state and 1st excited state energies and wave functions were calculated for systems of one or two electrons in a 2D and 3D potential well having a shape intermediate between a circle and a square or a sphere and a cube. One way to define such a potential well is with a step potential and a bounding surface of form $|x|^q+|y|^q+|z|^q = |r|^q$, which converts from a sphere to a cube when $q$ increases from $2$ to infinity. This kind of geometrical object is called a Lam\'{e} surface. The calculations were done either with implicit finite difference time stepping in the direction of negative imaginary time axis or with quantum diffusion Monte Carlo. The results demonstrate how the volume and depth of the potential well affect the $E_0$ more than the shape parameter $q$ does. Functions of two and three parameters were found to be sufficient for fitting an empirical graph to the ground state energy data points as a function of well depth $V_0$ or exponent $q$. The ground state and first excited state energy of one particle in a potential well of this type appeared to be very closely approximated with an exponential function depending on $q$, when the well depth and area or volume was kept constant while changing the value of $q$. The model is potentially useful for describing quantum dots that deviate from simple geometric shapes, or for demonstrating methods of computational quantum mechanics to undergraduate students.

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