Matching method and exact solvability of discrete PT-symmetric square wells

Details Matching method and exact solvability of discrete PT-symmetric square wells Matching method and exact solvability of discrete PT-symmetric square wells

2006-05-24

arxiv.org/abs/quant-ph/0605209v1

J.Phys. A39 (2006) 10247

Physics

Quantum Physics

25 pp, 3 figures

Scientific paper

10.1088/0305-4470/39/32/S23

Discrete PT-symmetric square wells are studied. Their wave functions are found proportional to classical Tshebyshev polynomials of complex argument. The compact secular equations for energies are derived giving the real spectra in certain intervals of non-Hermiticity strengths Z. It is amusing to notice that although the known square well re-emerges in the usual continuum limit, a twice as rich, upside-down symmetric spectrum is exhibited by all its present discretized predecessors.

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