$\mathcal{P}\mathcal{T}$ symmetric models with nonlinear pseudo supersymmetry

Abstract

By applying the higher order Darboux algorithm to an exactly solvable non Hermitian $\mathcal{P}\mathcal{T}$ symmetric potential, we obtain a hierarchy of new exactly solvable non Hermitian $\mathcal{P}\mathcal{T}$ symmetric potentials with real spectra. It is shown that the symmetry underlying the potentials so generated and the original one is {\it nonlinear pseudo supersymmetry}. We also show that this formalism can be used to generate a larger class of new solvable potentials when applied to non Hermitian systems.

18 pages

References in corpus (8)

• Complex Extension of Quantum Mechanics
• Pseudo-Hermiticity and Generalized PT- and CPT-Symmetries
• Nonlinear supersymmetry in Quantum Mechanics: algebraic properties and differential representation
• Calculation of the Hidden Symmetry Operator in PT-Symmetric Quantum Mechanics
• Second order SUSY transformations with `complex energies'
• Semiclassical Calculation of the C Operator in PT-Symmetric Quantum Mechanics
• Nonlinear superconformal symmetry of a fermion in the field of a Dirac monopole
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Cited by in corpus (5)

• Pseudo-Hermitian Representation of Quantum Mechanics
• Nonlinear Pseudo-Supersymmetry in the Framework of N-fold Supersymmetry
• Self-isospectral tri-supersymmetry in PT-symmetric quantum systems with pure imaginary periodicity
• Quasi-Hermitian supersymmetric extensions of a non-Hermitian oscillator Hamiltonian and of its generalizations
• Metric Operator For The Non-Hermitian Hamiltonian Model and Pseudo-Supersymmetry