Exactly solvable two-dimensional stationary Schrödinger operators obtained by the nonlocal Darboux transformation |
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Authors: | AG Kudryavtsev |
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Institution: | Institute of Applied Mechanics, Russian Academy of Sciences, Moscow 119991, Russia |
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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. |
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Keywords: | Darboux transformation Nonlocal variables Exactly solvable Schrö dinger equations |
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