Nonlocal supersymmetric deformations of periodic potentials

Details Nonlocal supersymmetric deformations of periodic potentials Nonlocal supersymmetric deformations of periodic potentials

2003-03-10

arxiv.org/abs/quant-ph/0303051v1

J.Phys.A35:4279-4291,2002

Physics

Quantum Physics

15 pages, latex, 9 postscript figures

Scientific paper

10.1088/0305-4470/35/19/309

Irreducible second-order Darboux transformations are applied to the periodic Schrodinger's operators. It is shown that for the pairs of factorization energies inside of the same forbidden band they can create new non-singular potentials with periodicity defects and bound states embedded into the spectral gaps. The method is applied to the Lame and periodic piece-wise transparent potentials. An interesting phenomenon of translational Darboux invariance reveals nonlocal aspects of the supersymmetric deformations.

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