PT-symmetric non-polynomial oscillators and hyperbolic potential with two known real eigenvalues in a SUSY framework

Abstract

Extending the supersymmetric method proposed by Tkachuk to the complex domain, we obtain general expressions for superpotentials allowing generation of quasi-exactly solvable PT-symmetric potentials with two known real eigenvalues (the ground state and first-excited state energies). We construct examples, namely those of complexified non-polynomial oscillators and of a complexified hyperbolic potential, to demonstrate how our scheme works in practice. For the former we provide a connection with the sl(2) method, illustrating the comparative advantages of the supersymmetric one.

14 pages, LaTeX, no figure

References in corpus (3)

• Generalized Continuity Equation and Modified Normalization in PT-Symmetric Quantum Mechanics
• Generating Complex Potentials with Real Eigenvalues in Supersymmetric Quantum Mechanics
• On a Lie algebraic approach of quasi-exactly solvable potentials with two known eigenstates

Cited by in corpus (7)

• Making Sense of Non-Hermitian Hamiltonians
• Pseudo-Supersymmetric Quantum Mechanics and Isospectral Pseudo-Hermi tian Hamiltonians
• Non-Hermitian Hamiltonians with real and complex eigenvalues in a Lie-algebraic framework
• The Quantum Mechanics SUSY Algebra: An Introductory Review
• The structure of supersymmetry in $\mathcal{P}\mathcal{T}$ symmetric quantum mechanics
• Supersymmetric Biorthogonal Quantum Systems
• A General Approach of Quasi-Exactly Solvable Schroedinger Equations with Three Known Eigenstates