arXiv:quant-ph/0201063 · Modern Physics Letters A

PT-SYMMETRIC NONPOLYNOMIAL OSCILLATORS AND HYPERBOLIC POTENTIAL WITH TWO KNOWN REAL EIGENVALUES IN A SUSY FRAMEWORK

Bijan Kumar Bagchi, C. Quesne

Published Mar 14, 2002• 9 citations

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 nonpolynomial 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.

DOI: 10.1142/s0217732302006734

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