Irreducible second order SUSY transformations between real and complex potentials

Abstract

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.

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

References in corpus (1)

• Nonlinear Pseudo-Supersymmetry in the Framework of N-fold Supersymmetry

Cited by in corpus (6)

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• Gamow-Siegert functions and Darboux-deformed short range potentials
• Optical potentials using resonance states in Supersymmetric Quantum Mechanics
• Quasi-Hermitian supersymmetric extensions of a non-Hermitian oscillator Hamiltonian and of its generalizations
• Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics
• Exact propagators for complex SUSY partners of real potentials