dorsal/arxiv
View SchemaNew set of exactly solvable complex potentials giving the real energies
| Authors | Miloslav Znojil |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9912079 |
| URL | https://arxiv.org/abs/quant-ph/9912079 |
Abstract
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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"abstract": "We deform the real potential of Poeschl and Teller by a shift of its\ncoordinate in imaginary direction. We show that the new model remains exactly\nsolvable. Its bound states are constructed in closed form. Wave functions are\ncomplex and proportional to Jacobi polynomials. Some of them diverge in the\nHermitian limit. In contrast, all their energies prove real and\nshift-independent. In this sense the lost Hermiticity of our family of\nHamiltonians seems replaced by their accidental PT symmetry.",
"arxiv_id": "quant-ph/9912079",
"authors": [
"Miloslav Znojil"
],
"categories": [
"quant-ph"
],
"title": "New set of exactly solvable complex potentials giving the real energies",
"url": "https://arxiv.org/abs/quant-ph/9912079"
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