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

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Author: Grafiati

Published: 4 June 2021

Last updated: 12 February 2022

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Nikitin, A. G., S. P. Onufriichuk, and V. I. Fushchich. "Higher symmetries of the Schr�dinger equation." Theoretical and Mathematical Physics 91, no. 2 (May 1992): 514–21. http://dx.doi.org/10.1007/bf01018849.

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12

林, 学好. "Difference Scheme of Nonlinear Schr?dinger Equation." Pure Mathematics 11, no. 04 (2021): 496–502. http://dx.doi.org/10.12677/pm.2021.114063.

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13

Okino, Takahisa. "Correlation between Diffusion Equation and Schrödinger Equation." Journal of Modern Physics 04, no. 05 (2013): 612–15. http://dx.doi.org/10.4236/jmp.2013.45088.

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14

Dong, Ming, and Theodore Simos. "A new high algebraic order efficient finite difference method for the solution of the Schrödinger equation." Filomat 31, no. 15 (2017): 4999–5012. http://dx.doi.org/10.2298/fil1715999d.

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The development of a new five-stages symmetric two-step method of fourteenth algebraic order with vanished phase-lag and its first, second, third and fourth derivatives is analyzed in this paper. More specifically: (1) we will present the development of the new method, (2) we will determine the local truncation error (LTE) of the new proposed method, (3) we will analyze the local truncation error based on the radial time independent Schr?dinger equation, (4) we will study the stability and the interval of periodicity of the new proposed method based on a scalar test equation with frequency different than the frequency of the scalar test equation used for the phase-lag analysis, (5) we will test the efficiency of the new obtained method based on its application on the coupled differential equations arising from the Schr?dinger equation.

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15

Sj�lin, Per. "Regularity of solutions to the Schr�dinger equation." Duke Mathematical Journal 55, no. 3 (September 1987): 699–715. http://dx.doi.org/10.1215/s0012-7094-87-05535-9.

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16

El-Mennaoui, O., and V. Keyantuo. "On the Schr�dinger equation inL p spaces." Mathematische Annalen 304, no. 1 (January 1996): 293–302. http://dx.doi.org/10.1007/bf01446295.

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17

Lebowitz, Joel L., Harvey A. Rose, and Eugene R. Speer. "Statistical mechanics of the nonlinear Schr�dinger equation." Journal of Statistical Physics 50, no. 3-4 (February 1988): 657–87. http://dx.doi.org/10.1007/bf01026495.

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18

Chopik, V. I. "Non-Lie reduction of nonlinear Schr�dinger equation." Ukrainian Mathematical Journal 43, no. 11 (November 1991): 1396–400. http://dx.doi.org/10.1007/bf01067277.

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19

Bagrov, V. G., B. F. Samsonov, and L. A. Shekoyan. "Darboux transformation for the nonsteady Schr�dinger equation." Russian Physics Journal 38, no. 7 (July 1995): 706–12. http://dx.doi.org/10.1007/bf00560273.

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20

Graffi, Sandro, and Thierry Paul. "The Schr�dinger equation and canonical perturbation theory." Communications in Mathematical Physics 108, no. 1 (March 1987): 25–40. http://dx.doi.org/10.1007/bf01210701.

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21

Gr�bert, B., and T. Kappeler. "Perturbations of the Defocusing Nonlinear Schr�dinger Equation." Milan Journal of Mathematics 71, no. 1 (September 1, 2003): 141–74. http://dx.doi.org/10.1007/s00032-002-0018-2.

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22

Bibikov, P. N., and V. O. Tarasov. "Boundary-value problem for nonlinear Schr�dinger equation." Theoretical and Mathematical Physics 79, no. 3 (June 1989): 570–79. http://dx.doi.org/10.1007/bf01016541.

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23

Orlov, A. Yu, and E. I. Shul'man. "Additional symmetries of the nonlinear Schr�dinger equation." Theoretical and Mathematical Physics 64, no. 2 (August 1985): 862–66. http://dx.doi.org/10.1007/bf01017968.

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24

Bogolyubov, N. M., and V. E. Korepin. "Quantum nonlinear Schr�dinger equation on a lattice." Theoretical and Mathematical Physics 66, no. 3 (March 1986): 300–305. http://dx.doi.org/10.1007/bf01018229.

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25

Guiasu, Silviu. "Deducing the Schr�dinger equation from minimum ?2." International Journal of Theoretical Physics 31, no. 7 (July 1992): 1153–76. http://dx.doi.org/10.1007/bf00673918.

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26

Roy, Swapna, and A. Roy Chowdhury. "Prolongation theory. A new nonlinear Schr�dinger equation." International Journal of Theoretical Physics 26, no. 7 (July 1987): 707–14. http://dx.doi.org/10.1007/bf00670578.

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27

Volobuev, A. N., and A. P. Tolstonogov. "Nonlinear schr�dinger equation in a hydroelasticity problem." Journal of Engineering Physics and Thermophysics 66, no. 2 (February 1994): 199–202. http://dx.doi.org/10.1007/bf00862722.

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28

Braun, M. A. "Relationship between a quasipotential equation and a Schr�dinger equation." Theoretical and Mathematical Physics 72, no. 3 (September 1987): 958–64. http://dx.doi.org/10.1007/bf01018302.

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29

Zareski, David. "Relativistic Completion of Schrodinger’s Quantum Mechanics by the Ether Theory." Applied Physics Research 11, no. 4 (July 15, 2019): 52. http://dx.doi.org/10.5539/apr.v11n4p52.

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One recalls that we have shown in our precedent publications that the ether is an elastic isotropic medium. One presents the exact equation and its non-relativistic approximation that govern the ether in presence of a Schwarzschild-Coulomb field to which is submitted a Par(m,e)  (particle of mass m  and of electric charge e ). We present the exact relativistic solution of this exact equation in the circular case. We prove that the Schrödinger equation is such a non-relativistic approximation, that is, is a particular case of the ether elasticity theory. One recalls that the Schrödinger equation was obtained by the use of operators and not from the theory of elasticity. It follows that this manner of obtaining this equation from operators is arbitrary and does not permit to obtain its complete relativistic form, but permits to reach absurd conclusions as, e.g., the cat that, at the same moment, is alive and dead. One shows then that other results ensuing from the Schrödinger equation are particular cases of the non-relativistic equation that governs the elastic ether, like for example: the Bohr-Sommerfeld condition, and the eigenstates function equation.

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30

Grimalsky, Volodymyr, Outmane Oubram, Svetlana Koshevaya, and Christian Castrejon-Martinez. "Thomas-Fermi method for computing the electron spectrum and wave functions of highly doped quantum wires in n-Si." Facta universitatis - series: Electronics and Energetics 28, no. 1 (2015): 103–11. http://dx.doi.org/10.2298/fuee1501103g.

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The application of the Thomas-Fermi method to calculate the electron spectrum in quantum wells formed by highly doped n-Si quantum wires is presented under finite temperatures where the many-body effects, like exchange, are taken into account. The electron potential energy is calculated initially from a single equation. Then the electron energy sub-levels and the wave functions within the potential well are simulated from the Schr?dinger equation. For axially symmetric wave functions the shooting method has been used. Two methods have been applied to solve the Schr?dinger equation in the case of the anisotropic effective electron mass, the variation method and the iteration procedure for the eigenvectors of the Hamiltonian matrix.

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31

Bagrov, V. G., B. F. Samsonov, and A. V. Shapovalov. "Free Schr�dinger equation analyzed in terms of the wave equation." Soviet Physics Journal 33, no. 7 (July 1990): 600–604. http://dx.doi.org/10.1007/bf00899111.

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32

SHANG Wei, 尚维, and 张建勇 ZHANG Jian-yong. "Multimode Local Error Criterion of Nonlinear Schrdinger Equation." ACTA PHOTONICA SINICA 48, no. 4 (2019): 406001. http://dx.doi.org/10.3788/gzxb20194804.0406001.

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33

M-Ali, Mujahid Abd Elmjed. "Stability Solution of the Nonlinear Schrödinger Equation." International Journal of Modern Nonlinear Theory and Application 02, no. 02 (2013): 122–29. http://dx.doi.org/10.4236/ijmnta.2013.22015.

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34

Morales, J., J. García-Martínez, J. García-Ravelo, and J. J. Peña. "Exactly Solvable Schrödinger Equation with Hypergeometric Wavefunctions." Journal of Applied Mathematics and Physics 03, no. 11 (2015): 1454–71. http://dx.doi.org/10.4236/jamp.2015.311173.

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35

Lin, Bin. "Spline Solution for the Nonlinear Schrödinger Equation." Journal of Applied Mathematics and Physics 04, no. 08 (2016): 1600–1609. http://dx.doi.org/10.4236/jamp.2016.48170.

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36

Robbiano, Luc, and Claude Zuily. "Microlocal analytic smoothing effect for the Schr�dinger equation." Duke Mathematical Journal 100, no. 1 (October 1999): 93–129. http://dx.doi.org/10.1215/s0012-7094-99-10003-2.

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37

McKean, H. P., and K. L. Vaninsky. "Action-angle variables for the cubic Schr�dinger equation." Communications on Pure and Applied Mathematics 50, no. 6 (June 1997): 489–562. http://dx.doi.org/10.1002/(sici)1097-0312(199706)50:6<489::aid-cpa1>3.0.co;2-4.

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38

Haller, G. "Homoclinic jumping in the perturbed nonlinear Schr�dinger equation." Communications on Pure and Applied Mathematics 52, no. 1 (January 1999): 1–47. http://dx.doi.org/10.1002/(sici)1097-0312(199901)52:1<1::aid-cpa1>3.0.co;2-s.

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39

Nicola, S. De. "Conservation laws for the non-linear Schr dinger equation." Pure and Applied Optics: Journal of the European Optical Society Part A 2, no. 1 (January 1993): 5–7. http://dx.doi.org/10.1088/0963-9659/2/1/002.

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40

Tarasov, V. O. "Boundary-value problem for the nonlinear Schr�dinger equation." Journal of Soviet Mathematics 54, no. 3 (April 1991): 958–67. http://dx.doi.org/10.1007/bf01101127.

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41

Ulmer, W. "A solution spectrum of the nonlinear schr�dinger equation." International Journal of Theoretical Physics 27, no. 6 (June 1988): 767–85. http://dx.doi.org/10.1007/bf00669321.

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42

Klimontovich, Yu L. "On the statistical derivation of the Schr�dinger equation." Theoretical and Mathematical Physics 97, no. 1 (October 1993): 1111–25. http://dx.doi.org/10.1007/bf01014804.

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43

B�gout, Pascal. "Maximum decay rate for the nonlinear Schr�dinger equation." Nonlinear Differential Equations and Applications NoDEA 11, no. 4 (December 2004): 451–67. http://dx.doi.org/10.1007/s00030-004-2003-7.

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44

Ganelin, P. V., and V. I. Pupyshev. "Analytic properties of solution of electronic Schr�dinger equation." Theoretical and Mathematical Physics 88, no. 1 (July 1991): 694–98. http://dx.doi.org/10.1007/bf01016335.

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45

Chuburin, Yu P. "Multidimensional discrete Schr�dinger equation with limit periodic potential." Theoretical and Mathematical Physics 102, no. 1 (January 1995): 53–59. http://dx.doi.org/10.1007/bf01017455.

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46

Wignall, J. W. G. "The nonrelativistic Schr�dinger equation in ?quasi-classical? theory." Foundations of Physics 17, no. 2 (February 1987): 123–47. http://dx.doi.org/10.1007/bf00733204.

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47

陈, 红宇. "Conformal Momentum of Damped Stochastic Nonlinear Schr?dinger Equation." Advances in Applied Mathematics 10, no. 04 (2021): 865–70. http://dx.doi.org/10.12677/aam.2021.104094.

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48

Omuraliev, Asan, and Kyzy Esengul. "Asymptotics of solution to the nonstationary Schrödinger equation." Filomat 33, no. 5 (2019): 1361–68. http://dx.doi.org/10.2298/fil1905361o.

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The Cauchy problem with a rapidly oscillating initial condition for the homogeneous Schr?dinger equation was studied in [5]. Continuing the research ideas of this work and [3], in this paper we construct the asymptotic solution to the following mixed problem for the nonstationary Schr?dinger equation: Lhu ? ih?tu + h2?2xu-b(x,t)u = f(x,t), (x,t) ? ??= (0,1) x (0,T], u|t=0 = g(x), u|x=0 = u|x=1 = 0, (1) where h > 0 is a Planck constant, u = u(x,t,h). b(x,t), f(x,t) ? C??(??), g(x) ? C? [0,1] are given functions. The similar problem was studied in [7, 8] when the Plank constant is absent in the first term of the equation and asymptotics of solution of any order with respect to a parameter was constructed. In this paper, we use a generalization of the method used in [7].

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49

Ohno, Kaoru. "Time-Dependent Schrödinger Equation Approach and Bethe-Salpeter Equation Approach." MATERIALS TRANSACTIONS 48, no. 4 (2007): 649–52. http://dx.doi.org/10.2320/matertrans.48.649.

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50

Samsonov, B. F., and I. N. Ovcharov. "Potentials reducing the one-dimensional Schr�dinger equation to the Mathieu equation." Russian Physics Journal 37, no. 6 (June 1994): 574–77. http://dx.doi.org/10.1007/bf00558704.

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