Second Order Darboux Displacements

Details Second Order Darboux Displacements Second Order Darboux Displacements

2003-07-21

arxiv.org/abs/quant-ph/0307146v1

J. Phys. A: Math. Gen. 36 (2003) 10053--10069

Physics

Quantum Physics

Scientific paper

10.1088/0305-4470/36/39/306

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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