Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10727825 | Physics Letters A | 2013 | 13 Pages |
Abstract
The Fokker-Planck equation associated with the two-dimensional stationary Schrödinger equation has the conservation law form that yields a pair of potential equations. The special form of Darboux transformation of the potential equations system is considered. As the potential variable is a nonlocal variable for the Schrödinger equation that provides the nonlocal Darboux transformation for the Schrödinger equation. This nonlocal transformation is applied for obtaining of the exactly solvable two-dimensional stationary Schrödinger equations. The examples of exactly solvable two-dimensional stationary Schrödinger operators with smooth potentials decaying at infinity are obtained.
Keywords
Related Topics
Physical Sciences and Engineering
Physics and Astronomy
Physics and Astronomy (General)
Authors
A.G. Kudryavtsev,