1303.5858 (Andrey Kudryavtsev)

The nonlocal Darboux transformation of the 2D stationary Schrödinger
equation and its relation to the Moutard transformation    [PDF]

Andrey Kudryavtsev

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 particular case of the nonlocal Darboux transformation provides the Moutard transformation. New examples of exactly solvable two - dimensional stationary Schr\"odinger operators with smooth potentials are obtained as an application of the nonlocal Darboux transformation.

View original: http://arxiv.org/abs/1303.5858