The nonlocal Darboux transformation of the stationary axially symmetric Schr\"odinger equation and generalized Moutard transformation
Abstract
The nonlocal Darboux transformation of the stationary axially symmetric Schr\"odinger equation is considered. It is shown that a special case of the nonlocal Darboux transformation provides the generalization of the Moutard transformation. Formulae for the generalized Moutard transformation are obtained. New examples of two - dimensional potencials and exact solutions for the stationary axially symmetric Schr\"odinger equation are obtained as an application of the generalized Moutard transformation.
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