PT symmetry of a conditionally exactly solvable potential

Abstract

A conditionally exactly solvable potential, the supersymmetric partner of the harmonic oscillator is investigated in the PT-symmetric setting. It is shown that a number of properties characterizing shape-invariant and Natanzon-class potentials generated by an imaginary coordinate shift $x-\mathrm{i}\epsilon$ also hold for this potential outside the Natanzon class.

8 pages, 4 figures, To appear in Physics Letters A

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• Non-linear Supersymmetry for non-Hermitian, non-diagonalizable Hamiltonians: I. General properties
• Solvable PT-symmetric model with a tunable interspersion of non-merging levels
• A conditionally exactly solvable generalization of the inverse square root potential
• The structure of supersymmetry in $\mathcal{P}\mathcal{T}$ symmetric quantum mechanics
• Classical oscillator with position-dependent mass in a complex domain
• A new solvable complex PT-symmetric potential
• Exactly solvable $\mathcal{P}\mathcal{T}$-symmetric models in two dimensions
• L2 series solutions of the Dirac equation for power-law potentials at rest mass energy
• Crypto-Harmonic Oscillator in Higher Dimensions: Classical and Quantum Aspects