The nonlocal Darboux transformation of the 2D stationary Schr\"odinger equation and its relation to the Moutard transformation
Abstract
The nonlocal Darboux transformation of the two - dimensional stationary Schr\"odinger equation is considered and its relation to the Moutard transformation is established. It is shown that a special case of the nonlocal Darboux transformation provides the Moutard transformation. New examples of solvable two - dimensional stationary Schr\"odinger operators with smooth potentials are obtained as an application of the nonlocal Darboux transformation.
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