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PT-symmetric nonpolynomial oscillators and hyperbolic potential with two known real eigenvalues in a susy framework
Published in
Volume: 17
Issue: 8
Pages: 463 - 473
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.
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