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

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

2002-01-16

arxiv.org/abs/quant-ph/0201063v1

Mod.Phys.Lett. A17 (2002) 463-473

Physics

Quantum Physics

14 pages, LaTeX, no figure

Scientific paper

10.1142/S0217732302006734

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.

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