PT-symmetric supersymmetry in a solvable short-range model

Abstract

The simplest purely imaginary and piecewise constant $\mathcal{P}\mathcal{T}$-symmetric potential located inside a larger box is studied. Unless its strength exceeds a certain critical value, all the spectrum of its bound states remains real and discrete. We interpret such a model as an initial element of the generalized non-Hermitian Witten's hierarchy of solvable Hamiltonians and construct its first supersymmetric (SUSY) partner in closed form.

3 figures, 1 table

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Cited by in corpus (9)

• Discrete PT-symmetric models of scattering
• Fundamental length in quantum theories with PT-symmetric Hamiltonians
• Conditional observability
• Fundamental length in quantum theories with PT-symmetric Hamiltonians II: The case of quantum graphs
• Supersymmetric Biorthogonal Quantum Systems
• Confluences of exceptional points and a systematic classification of quantum catastrophes
• Anomalous Faraday effect in a $\mathcal{P}\mathcal{T}$-symmetric dielectric slab
• Hermitian--to--quasi-Hermitian quantum phase transitions
• CPT-symmetric discrete square well