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Discrete PT-symmetric square-well oscillators

Miloslav Znojil
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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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Miloslav Znojil. 2005-11-11. Discrete PT-symmetric square-well oscillators. https://arxiv.org/abs/quant-ph/0511110

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