Analytic energies and wave functions of the two-dimensional Schrödinger equation: ground state of two-dimensional quartic potential and classification of solutions-Reference-Cited by-同舟云学术

Analytic energies and wave functions of the two-dimensional Schrödinger equation: ground state of two-dimensional quartic potential and classification of solutions

Published:2012-06 Issue:6 Volume:90 Page:503-513
ISSN:0008-4204
Container-title:Canadian Journal of Physics
language:en
Short-container-title:Can. J. Phys.

Author:

Tichý Vladimír¹,Kuběna Aleš Antonín²,Skála Lubomír¹³

Affiliation:

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

2. Academy of Sciences of the Czech Republic, Institute of Information Theory and Automation, Pod Vodárenskou věží 4, 18208, Prague 8, Czech Republic.

3. Department of Applied Mathematics, University of Waterloo, Waterloo, ON N2L 3G1, Canada.

Abstract

New analytic solutions of the two-dimensional Schrödinger equation with a two-dimensional fourth-order polynomial (i.e., quartic) potential are derived and discussed. The solutions represent the ground state energies and the corresponding wave functions. In general, the obtained results cannot be reduced to two one-dimensional cases.

Publisher

Canadian Science Publishing

Subject

General Physics and Astronomy

Link

http://www.nrcresearchpress.com/doi/pdf/10.1139/p2012-046

Reference11 articles.

1. Quantum anharmonic oscillator in the Heisenberg picture and multiple scale techniques

2. A SUSY approach for investigation of two-dimensional quantum mechanical systems

3. Exact wave functions from classical orbits: The isotropic harmonic oscillator and semiclassical applications

4. Exact wave functions from classical orbits. II. The Coulomb, Morse, Rosen-Morse, and Eckart systems

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