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

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Cited by in corpus (13)

• Spectral singularities in PT-symmetric periodic finite-gap systems
• Shape-invariant quantum Hamiltonian with position-dependent effective mass through second order supersymmetry
• Gamow-Siegert functions and Darboux-deformed short range potentials
• Self-isospectral tri-supersymmetry in PT-symmetric quantum systems with pure imaginary periodicity
• 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
• Spectral Design for Matrix Hamiltonians: Different Methods of Constructing of a Matrix Intertwining Operator
• Exact propagators for complex SUSY partners of real potentials
• Polynomial Supersymmetry for Matrix Hamiltonians
• Minimal Realizations of Supersymmetry for Matrix Hamiltonians
• Equivalent Hermitian operator from supersymmetric quantum mechanics
• Polynomial supersymmetry for matrix Hamiltonians: proofs