Relevant bibliographies by topics / Schr??dinger equation

Academic literature on the topic 'Schr??dinger equation'

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Published: 4 June 2021
Last updated: 12 February 2022

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Journal articles on the topic "Schr??dinger equation"

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Previato, Emma. "nonlinear Schr�dinger equation." Duke Mathematical Journal 52, no. 2 (June 1985): 329–77. http://dx.doi.org/10.1215/s0012-7094-85-05218-4.

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Obaya, Rafael, and Miguel Paramio. "almost-periodic Schr�dinger equation." Duke Mathematical Journal 66, no. 3 (June 1992): 521–52. http://dx.doi.org/10.1215/s0012-7094-92-06617-8.

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Vladimirov, V. S., and I. V. Volovich. "P-adic Schr�dinger-type equation." Letters in Mathematical Physics 18, no. 1 (July 1989): 43–53. http://dx.doi.org/10.1007/bf00397056.

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Agirseven, Deniz. "On the stability of the Schrödinger equation with time delay." Filomat 32, no. 3 (2018): 759–66. http://dx.doi.org/10.2298/fil1803759a.

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In the present paper, the initial value problem for the Schr?dinger equation with time delay in a Hilbert space is investigated. Theorems on stability estimates for the solution of the problem are established. The applications of theorems for three types of Schr?dinger problems are provided.
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Li Xiang－Zheng, Zhang Jin－Liang, Wang Yue－Ming, and Wang Ming－Liang. "Envelope solutions to nonlinear Schr?dinger equation." Acta Physica Sinica 53, no. 12 (2004): 4045. http://dx.doi.org/10.7498/aps.53.4045.

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Vaninsky, K. L. "space for the cubic Schr�dinger equation." Duke Mathematical Journal 92, no. 2 (April 1998): 381–402. http://dx.doi.org/10.1215/s0012-7094-98-09211-0.

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Kulish, P. P. "Quantum OSP-invariant nonlinear Schr�dinger equation." Letters in Mathematical Physics 10, no. 1 (July 1985): 87–93. http://dx.doi.org/10.1007/bf00704591.

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Frolov, N. N. "Schr�dinger equation in a Hilbert space." Mathematical Notes of the Academy of Sciences of the USSR 37, no. 3 (March 1985): 215–19. http://dx.doi.org/10.1007/bf01158743.

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Its, A. R., A. V. Rybin, and M. A. Sall'. "Exact integration of nonlinear Schr�dinger equation." Theoretical and Mathematical Physics 74, no. 1 (January 1988): 20–32. http://dx.doi.org/10.1007/bf01018207.

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Nagiev, Sh M. "Difference Schr�dinger equation andq-oscillator model." Theoretical and Mathematical Physics 102, no. 2 (February 1995): 180–87. http://dx.doi.org/10.1007/bf01040399.

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Dissertations / Theses on the topic "Schr??dinger equation"

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Grice, Glenn Noel Mathematics UNSW. "Constant speed flows and the nonlinear Schr??dinger equation." Awarded by:University of New South Wales. Mathematics, 2004. http://handle.unsw.edu.au/1959.4/20509.

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This thesis demonstrates how the geometric connection between the integrable Heisenberg spin equation, the nonlinear Schr??dinger equation and fluid flows with constant velocity magnitude along individual streamlines may be exploited. Specifically, we are able to construct explicitly the complete class of constant speed flows where the constant pressure surfaces constitute surfaces of revolution. This class is undoubtedly important as it contains many of the specific cases discussed earlier by other authors.
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Aydin, Ayhan. "Geometric Integrators For Coupled Nonlinear Schrodinger Equation." Phd thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/12605773/index.pdf.

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Multisymplectic integrators like Preissman and six-point schemes and a semi-explicit symplectic method are applied to the coupled nonlinear Schrö
dinger equations (CNLSE). Energy, momentum and additional conserved quantities are preserved by the multisymplectic integrators, which are shown using modified equations. The multisymplectic schemes are backward stable and non-dissipative. A semi-explicit method which is symplectic in the space variable and based on linear-nonlinear, even-odd splitting in time is derived. These methods are applied to the CNLSE with plane wave and soliton solutions for various combinations of the parameters of the equation. The numerical results confirm the excellent long time behavior of the conserved quantities and preservation of the shape of the soliton solutions in space and time.
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Mugassabi, Souad. "Schrödinger equation with periodic potentials." Thesis, University of Bradford, 2010. http://hdl.handle.net/10454/4895.

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The Schrödinger equation ... is considered. The solution of this equation is reduced to the problem of finding the eigenvectors of an infinite matrix. The infinite matrix is truncated to a finite matrix. The approximation due to the truncation is carefully studied. The band structure of the eigenvalues is shown. The eigenvectors of the multiwells potential are presented. The solutions of Schrödinger equation are calculated. The results are very sensitive to the value of the parameter y. Localized solutions, in the case that the energy is slightly greater than the maximum value of the potential, are presented. Wigner and Weyl functions, corresponding to the solutions of Schrödinger equation, are also studied. It is also shown that they are very sensitive to the value of the parameter y.
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Koca, Burcu. "Studies On The Perturbation Problems In Quantum Mechanics." Master's thesis, METU, 2004. http://etd.lib.metu.edu.tr/upload/12604930/index.pdf.

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In this thesis, the main perturbation problems encountered in quantum mechanics have been studied.Since the special functions and orthogonal polynomials appear very extensively in such problems, we emphasize on those topics as well. In this context, the classical quantum mechanical anharmonic oscillators described mathematically by the one-dimensional Schr¨
odinger equation have been treated perturbatively in both finite and infinite intervals, corresponding to confined and non-confined systems, respectively.
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Alici, Haydar. "Pseudospectral Methods For Differential Equations: Application To The Schrodingertype Eigenvalue Problems." Master's thesis, METU, 2003. http://etd.lib.metu.edu.tr/upload/1086198/index.pdf.

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In this thesis, a survey on pseudospectral methods for differential equations is presented. Properties of the classical orthogonal polynomials required in this context are reviewed. Differentiation matrices corresponding to Jacobi, Laguerre,and Hermite cases are constructed. A fairly detailed investigation is made for the Hermite spectral methods, which is applied to the Schrö
dinger eigenvalue equation with several potentials. A discussion of the numerical results and comparison with other methods are then introduced to deduce the effciency of the method.
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Alici, Haydar. "A General Pseudospectral Formulation Of A Class Of Sturm-liouville Systems." Phd thesis, METU, 2010. http://etd.lib.metu.edu.tr/upload/12612435/index.pdf.

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In this thesis, a general pseudospectral formulation for a class of Sturm-Liouville eigenvalue problems is consructed. It is shown that almost all, regular or singular, Sturm-Liouville eigenvalue problems in the Schrö
dinger form may be transformed into a more tractable form. This tractable form will be called here a weighted equation of hypergeometric type with a perturbation (WEHTP) since the non-weighted and unperturbed part of it is known as the equation of hypergeometric type (EHT). It is well known that the EHT has polynomial solutions which form a basis for the Hilbert space of square integrable functions. Pseudospectral methods based on this natural expansion basis are constructed to approximate the eigenvalues of WEHTP, and hence the energy eigenvalues of the Schrö
dinger equation. Exemplary computations are performed to support the convergence numerically.
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Ozdemir, Sevilay. "Bose-einstein Condensation At Lower Dimensions." Master's thesis, METU, 2004. http://etd.lib.metu.edu/upload/755959/index.pdf.

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In this thesis, the properties of the Bose-Einstein condensation (BEC) in low dimensions are reviewed. Three dimensional weakly interacting Bose systems are examined by the variational method. The effects of both the attractive and the repulsive interatomic forces are studied. Thomas-Fermi approximation is applied to find the ground state energy and the chemical potential. The occurrence of the BEC in low dimensional systems, is studied for ideal gases confined by both harmonic and power-law potentials. The properties of BEC in highly anisotropic trap are investigated and the conditions for reduced dimensionality are derived.
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Bucurgat, Mahmut. "Study Of One Dimensional Position Dependent Effective Mass Problem In Some Quantum Mechanical Systems." Phd thesis, METU, 2008. http://etd.lib.metu.edu.tr/upload/2/12609405/index.pdf.

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The one dimensional position dependent effective mass problem is studied by solving the Schrö
dinger equation for some well known potentials, such as the deformed Hulthen, the Mie, the Kratzer, the pseudoharmonic, and the Morse potentials. Nikiforov-Uvarov method is used in the calculations to get energy eigenvalues and the corresponding wave functions exactly. By introducing a free parameter in the transformation of the wave function, the position dependent effective mass problem is reduced to the solution of the Schrö
dinger equation for the constant mass case. At the same time, the deformed Hulthen potential is solved for the position dependent effective mass case by applying the method directly. The Morse potential is also solved for a mass distribution function, such that the solution can be reduced to the constant mass case.
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Moşincat, Răzvan Octavian. "Well-posedness of the one-dimensional derivative nonlinear Schrödinger equation." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/33244.

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This thesis is concerned with the well-posedness of the one-dimensional derivative non-linear Schrodinger equation (DNLS). In particular, we study the initial-value problem associated to DNLS with low-regularity initial data in two settings: (i) on the torus (namely with the periodic boundary condition) and (ii) on the real line. Our first main goal is to study the global-in-time behaviour of solutions to DNLS in the periodic setting, where global well-posedness is known to hold under a small mass assumption. In Chapter 2, we relax the smallness assumption on the mass and establish global well-posedness of DNLS for smooth initial data. In Chapter 3, we then extend this result for rougher initial data. In particular, we employ the I-method introduced by Colliander, Keel, Staffilani, Takaoka, and Tao and show the global well-posedness of the periodic DNLS at the end-point regularity. In the implementation of the I-method, we apply normal form reductions to construct higher order modified energy functionals. In Chapter 4, we turn our attention to the uniqueness of solutions to DNLS on the real line. By using an infinite iteration of normal form reductions introduced by Guo, Kwon, and Oh in the context of one-dimensional cubic NLS on the torus, we construct solutions to DNLS without using any auxiliary function space. As a result, we prove the unconditional uniqueness of solutions to DNLS on the real line in an almost end-point regularity.
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Deng, Shengfu. "A Spatial Dynamic Approach to Three-Dimensional Gravity-Capillary Water Waves." Diss., Virginia Tech, 2008. http://hdl.handle.net/10919/28254.

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Three-dimensional gravity-capillary steady waves on water of finite-depth, which are uniformly translating in a horizontal propagation direction and periodic in a transverse direction, are considered. The exact Euler equations are formulated as a spatial dynamic system in which the variable used for the propagating direction is the time-like variable. The existence of the solutions of the system is determined by two non-dimensional constants: the Bond number b and λ (the inverse of the square of the Froude number). The property of Sobolev spaces and the spectral analysis show that the spectrum of the linear part consists of isolated eigenvalues of finite algebraic multiplicity and the number of purely imaginary eigenvalues are finite. The distribution of eigenvalues is described by b and λ. Assume that C1 is the curve in (b,λ)-plane on which the first two eigenvalues for three-dimensional waves collide at the imaginary axis, and that the intersection point of the curve C1 with the line λ=1 is (b0,1) where b0>0. Two cases (b0,1) and (b,λ) â C1 where 0< b< b0 are investigated. A center-manifold reduction technique and a normal form analysis are applied to show that for each case the dynamical system can be reduced to a system of ordinary differential equations with finite dimensions. The dominant system for the case (b0,1) is coupled Schrödinger-KdV equations while it is a Schrödinger equation for another case (b,λ) â C1. Then, from the existence of the homoclinic orbit connecting to the two-dimensional periodic solution (called generalized solitary wave) for the dominant system, it is obtained that such generalized solitary wave solution persists for the original system by using the perturbation method and adjusting some appropriate constants.
Ph. D.
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Books on the topic "Schr??dinger equation"

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Casdagli, Martin. Symbolic dynamics for the renormalization map of a quasiperiodic Schro dinger equation and periodic orbits for dissipative twist maps. [s.l.]: typescript, 1986.

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Kevrekidis, Panayotis G. The Discrete Nonlinear Schr Dinger Equation. Springer, 2009.

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Evolution Equations of Hyperbolic and Schr Dinger Type Progress in Mathematics. Birkh User, 2012.

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Book chapters on the topic "Schr??dinger equation"

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"On the Schr√∂dinger Equation of the Helium Atom." In V.A. Fock - Selected Works, 525–38. CRC Press, 2004. http://dx.doi.org/10.1201/9780203643204.ch15a.

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"On the Relation between the Integrals of the Quantum Mechanical Equations of Motion and the Schr√∂dinger Wave Equation." In V.A. Fock - Selected Works, 33–50. CRC Press, 2004. http://dx.doi.org/10.1201/9780203643204.ch2b.

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"The One-dimensional Schro¨dinger Equations." In Quantum Mechanics, 108–35. CRC Press, 2015. http://dx.doi.org/10.1201/b19619-16.

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"The Three-dimensional Schro¨dinger Equations." In Quantum Mechanics, 136–59. CRC Press, 2015. http://dx.doi.org/10.1201/b19619-17.

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"Time‐dependent and time‐independent Schrö dinger equations." In Foundations for Nanoscience and Nanotechnology, 25–26. Boca Raton, FL : CRC Press, Taylor & Francis Group, [2017] |: CRC Press, 2017. http://dx.doi.org/10.1201/9781315381381-5.

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"1 On the Schro¨dinger equation of the helium atom." In V.A. Fock - Selected Works, 537–50. CRC Press, 2004. http://dx.doi.org/10.1201/9780203643204-42.

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"Higher-Order Schro¨dinger Equations: from“Blow-up” Zero Structures to Quasilinear Operators." In Blow-up for Higher-Order Parabolic, Hyperbolic, Dispersion and Schrodinger Equations, 487–96. Chapman and Hall/CRC, 2014. http://dx.doi.org/10.1201/b17415-66.

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"-2 On the relation between the integrals of the quantum mechanical equations of motion and the Schro¨dinger wave equation." In V.A. Fock - Selected Works, 45–62. CRC Press, 2004. http://dx.doi.org/10.1201/9780203643204-10.

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Conference papers on the topic "Schr??dinger equation"

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Golmankhaneh, Alireza Khalili, and Ahmad Jafarian. "About fuzzy Schrödinger equation." In 2014 International Conference on Fractional Differentiation and its Applications (ICFDA). IEEE, 2014. http://dx.doi.org/10.1109/icfda.2014.6967457.

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Deng, Li, and Peng-Fei Yao. "Boundary controllability for the semilinear Schrödinger equation." In 2009 Joint 48th IEEE Conference on Decision and Control (CDC) and 28th Chinese Control Conference (CCC). IEEE, 2009. http://dx.doi.org/10.1109/cdc.2009.5400019.

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Krstic, Miroslav, Bao-Zhu Guo, and Andrey Smyshlyaev. "Boundary controllers and observers for Schrödinger equation." In 2007 46th IEEE Conference on Decision and Control. IEEE, 2007. http://dx.doi.org/10.1109/cdc.2007.4435016.

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Sigalotti, Mario, Paolo Mason, Ugo Boscain, and Thomas Chambrion. "Generic controllability properties for the bilinear Schrödinger equation." In 2009 Joint 48th IEEE Conference on Decision and Control (CDC) and 28th Chinese Control Conference (CCC). IEEE, 2009. http://dx.doi.org/10.1109/cdc.2009.5399813.

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Zhang, Yuanyuan. "Exact Solutions for the Generalized Derivative Schrödinger Equation." In 2009 Ninth International Conference on Hybrid Intelligent Systems. IEEE, 2009. http://dx.doi.org/10.1109/his.2009.310.

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Tiu, Zian Cheak, Harith Ahmad, and Sulaiman Wadi Harun. "Generation of Cubic-Quintic nonlinear schrödinger equation dark pulse." In 2015 11th Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR). IEEE, 2015. http://dx.doi.org/10.1109/cleopr.2015.7376108.

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Chang, Der-Chen, Stephen S. T. Yau, and Ke-Pao Lin. "Schrödinger equation with quartic potential and nonlinear filtering problem." In 2009 Joint 48th IEEE Conference on Decision and Control (CDC) and 28th Chinese Control Conference (CCC). IEEE, 2009. http://dx.doi.org/10.1109/cdc.2009.5400128.

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Youying Wang and Jingsong He. "Singular solution of the variable coefficient nonlinear Schrödinger equation." In 2011 International Conference on Multimedia Technology (ICMT). IEEE, 2011. http://dx.doi.org/10.1109/icmt.2011.6002444.

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Shahzad, Asim, and M. Zafrullah. "Solitons Interaction and their Stability Based on Nonlinear Schrödinger Equation." In 2009 Second International Conference on Machine Vision. IEEE, 2009. http://dx.doi.org/10.1109/icmv.2009.38.

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Boussaid, Nabile, Marco Caponigro, and Thomas Chambrion. "Approximate controllability of the Schrödinger equation with a polarizability term." In 2012 IEEE 51st Annual Conference on Decision and Control (CDC). IEEE, 2012. http://dx.doi.org/10.1109/cdc.2012.6426619.

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