New Exactly Solvable Isospectral Partners for PT Symmetric Potentials

Abstract

We examine in detail the possibilty of applying Darboux transformation to non Hermitian hamiltonians. In particular we propose a simple method of constructing exactly solvable PT symmetric potentials by applying Darboux transformation to higher states of an exactly solvable PT symmetric potential. It is shown that the resulting hamiltonian and the original one are pseudo supersymmetric partners. We also discuss application of Darboux transformation to hamiltonians with spontaneously broken PT symmetry.

11 pages, 2 figures, To be published in Journal of Physics A (2004)

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• Complexified PSUSY and SSUSY interpretations of some PT-symmetric Hamiltonians possessing two series of real energy eigenvalues
• Non-Hermitian SUSY Hydrogen-like Hamiltonians with real spectra
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• Isospectral partners for a complex PT-invariant potential
• Supersymmetric quantum mechanics based on higher excited states
• Physical sectors of the confluent hypergeometric functions space

Cited by in corpus (6)

• Making Sense of Non-Hermitian Hamiltonians
• Bi-Orthogonal Approach to Non-Hermitian Hamiltonians with the Oscillator Spectrum: Generalized Coherent States for Nonlinear Algebras
• The structure of supersymmetry in $\mathcal{P}\mathcal{T}$ symmetric quantum mechanics
• Supersymmetric Biorthogonal Quantum Systems
• $\mathcal{P}\mathcal{T}$ symmetric models with nonlinear pseudo supersymmetry
• Instantaneous modulations in time-varying complex optical potentials