/ 03 07 14 6 v 1 2 1 Ju l 2 00 3 Second Order

نویسنده

  • B F Samsonov
چکیده

The potentials for a one dimensional Schrödinger 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 Schrödinger 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 Lamé-Ince potential is 2-SUSY invariant. Both Bloch solutions of the corresponding Schrödinger 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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تاریخ انتشار 2003