Irreducible second order SUSY transformations between real and complex potentials

Details Irreducible second order SUSY transformations between real and complex potentials Irreducible second order SUSY transformations between real and complex potentials

2006-02-13

arxiv.org/abs/quant-ph/0602101v3

Physics Letters A 358 (2006) 105-114

Physics

Quantum Physics

Thanks to M.V. Ioffee Ref. [13] is corrected in the second version

Scientific paper

10.1016/j.physleta.2006.04.109

Second order SUSY transformations between real and complex potentials for three important from physical point of view Sturm-Liouville problems, namely, problems with the Dirichlet boundary conditions for a finite interval, for a half axis and for the whole real line are analyzed. For every problem conditions on transformation functions are formulated when transformations are irreducible, i.e. when either the intermediate Hamiltonian is not well defined in the same Hilbert space as the initial and final Hamiltonians or its eigenfunctions cannot be obtained by applying transformation operator either on eigenfunctions of the initial Hamiltonian or on these of the final Hamiltonian. Obtained results are illustrated by numerous simple examples.

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