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Number of results

Journal

2014 | 12 | 10 | 730-736

Article title

Algebraic approach to non-separable two-dimensional Schrödinger equation: Ground states for polynomial and Morse-like potentials

Content

Title variants

Languages of publication

EN

Abstracts

EN
This paper presents a direct algebraic method of searching for analytic solutions of the two-dimensional time-independent Schrödinger equation that is impossible to separate into two one-dimensional ones. As examples, two-dimensional polynomial and Morse-like potentials are discussed. Analytic formulas for the ground state wave functions and the corresponding energies are presented. These results cannot be obtained by another known method.

Publisher

Journal

Year

Volume

12

Issue

10

Pages

730-736

Physical description

Dates

published
1 - 10 - 2014
online
16 - 8 - 2014

Contributors

  • Faculty of Electrical Engineering, Czech Technical University in Prague, Technická 2, 16627, Prague 6, Czech Republic
  • Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, 12116, Prague 2, Czech Republic
author
  • Faculty of Electrical Engineering, Czech Technical University in Prague, Technická 2, 16627, Prague 6, Czech Republic

References

  • [1] H. Nakatsuji, Phys. Rev. A 65, 052122/1 (2002) http://dx.doi.org/10.1103/PhysRevA.65.052122[Crossref]
  • [2] K. G. Kay, Phys. Rev. A 63, 042110/1 (2001) http://dx.doi.org/10.1103/PhysRevA.63.042110[Crossref]
  • [3] K. G. Kay, Phys. Rev. A 65, 032101/1 (2002) http://dx.doi.org/10.1103/PhysRevA.65.032101[Crossref]
  • [4] M. V Ioffe, J. Phys. A, Math. Gen. 37, 10363 (2004) http://dx.doi.org/10.1088/0305-4470/37/43/023[Crossref]
  • [5] M. Znojil, J. Phys. A, Math. Gen. 36, 7828 (2003)
  • [6] J. Dvořák, L. Skála, Collect. Czech. Chem. Commun. 63, 1161 (1998) http://dx.doi.org/10.1135/cccc19981161[Crossref]
  • [7] L. Skála, J. Č ížek, J. Dvořák, V. Špirko, Phys. Rev. A 53, 2009 (1996) http://dx.doi.org/10.1103/PhysRevA.53.2009[Crossref]
  • [8] L. Skála, J. Dvořák, V. Kapsa, Int. J. Theor. Phys. 36, 2953 (1997) http://dx.doi.org/10.1007/BF02435720[Crossref]
  • [9] V. Tichý, L. Skála, Collect. Czech. Chem. Commun., 73(10), 1327 (2008) http://dx.doi.org/10.1135/cccc20081327[Crossref]
  • [10] V. Tichý, L. Skála, Cent. Eur. J. Phys. 8, 519 (2010) http://dx.doi.org/10.2478/s11534-009-0127-4[Crossref]
  • [11] V. Tichý, A. A. Kuběna, L. Skála, Can. J. Phys. 90, 503 (2012) http://dx.doi.org/10.1139/p2012-046[Crossref]

Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.-psjd-doi-10_2478_s11534-014-0484-5
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