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

Vladimír Tichý; Lubomír Skála; René Hudec

doi:10.2478/s11534-014-0484-5

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Journal

Open Physics

2014 | 12 | 10 | 730-736

Article title

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

Authors

Vladimír Tichý , Lubomír Skála , René Hudec

Content

http://www.degruyter.com/view/j/phys.2014.12.issue-10/s11534-014-0484-5/s11534-014-0484-5.pdf [remote]

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Abstracts

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.

Keywords

algebraic methods analytical methods quantum mechanics

Publisher

De Gruyter Open

Journal

Open Physics

Year

2014

Volume

Issue

Pages

730-736

Physical description

Dates

published

1 - 10 - 2014

online

16 - 8 - 2014

References

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[3] K. G. Kay, Phys. Rev. A 65, 032101/1 (2002) http://dx.doi.org/10.1103/PhysRevA.65.032101[Crossref]
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[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

YADDA identifier

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

Identifiers

DOI

10.2478/s11534-014-0484-5