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Second Order Darboux Displacements

B F Samsonov·M L Glasser·J Negro·L M Nieto
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Abstract

The potentials for a one dimensional Schroedinger equation that are displaced along the x axis under second order Darboux transformations, called 2-SUSY invariant, are characterized in terms of a differential-difference equation. The solutions of the Schroedinger equation with such potentials are given analytically for any value of the energy. The method is illustrated by a two-soliton potential. It is proven that a particular case of the periodic Lame-Ince potential is 2-SUSY invariant. Both Bloch solutions of the corresponding Schroedinger equation equation are found for any value of the energy. A simple analytic expression for a family of two-gap potentials is derived.

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B F Samsonov, M L Glasser, J Negro, L M Nieto. 2003-07-21. Second Order Darboux Displacements. https://doi.org/10.1088/0305-4470/36/39/306

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