New set of exactly solvable complex potentials giving the real energies

Details New set of exactly solvable complex potentials giving the real energies New set of exactly solvable complex potentials giving the real energies

1999-12-16

arxiv.org/abs/quant-ph/9912079v1

Physics

Quantum Physics

submitted to Phys. Rev. A

Scientific paper

We deform the real potential of Poeschl and Teller by a shift of its coordinate in imaginary direction. We show that the new model remains exactly solvable. Its bound states are constructed in closed form. Wave functions are complex and proportional to Jacobi polynomials. Some of them diverge in the Hermitian limit. In contrast, all their energies prove real and shift-independent. In this sense the lost Hermiticity of our family of Hamiltonians seems replaced by their accidental PT symmetry.

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