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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, vladimir-tichy@email.cz
  • 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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