dorsal/arxiv
View SchemaDiscrete PT-symmetric square-well oscillators
| Authors | Miloslav Znojil |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0511110 |
| URL | https://arxiv.org/abs/quant-ph/0511110 |
Abstract
Exact solvability of the discretized N-point version of the PT-symmetric square-well model is pointed out. Its wave functions are found proportional to the classical Tshebyshev polynomials of a complex argument. At all N a compact secular equation is derived giving the real spectrum of energies at any non-Hermiticity strength Z below its finite and weakly N-dependent critical value. In the limit of vanishing Z the model degenerates to a Hermitian Hueckel Hamiltonian.
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"abstract": "Exact solvability of the discretized N-point version of the PT-symmetric\nsquare-well model is pointed out. Its wave functions are found proportional to\nthe classical Tshebyshev polynomials of a complex argument. At all N a compact\nsecular equation is derived giving the real spectrum of energies at any\nnon-Hermiticity strength Z below its finite and weakly N-dependent critical\nvalue. In the limit of vanishing Z the model degenerates to a Hermitian Hueckel\nHamiltonian.",
"arxiv_id": "quant-ph/0511110",
"authors": [
"Miloslav Znojil"
],
"categories": [
"quant-ph"
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"title": "Discrete PT-symmetric square-well oscillators",
"url": "https://arxiv.org/abs/quant-ph/0511110"
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