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

• Authors: Vladimír Tichý , Lubomír Skála , René Hudec
• 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.

Keywords

EN

algebraic methods; analytical methods; quantum mechanics

• Journal: Open Physics
• Year: 2014
• Volume: 12
• Issue: 10
• Pages: 730-736

Dates

published

1 - 10 - 2014

online

16 - 8 - 2014

Contributors

author

Vladimír Tichý

• Faculty of Electrical Engineering, Czech Technical University in Prague, Technická 2, 16627, Prague 6, Czech Republic,

author

Lubomír Skála

• Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, 12116, Prague 2, Czech Republic

author

René Hudec

• 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]

Identifiers

DOI

10.2478/s11534-014-0484-5