2005/11/11 by Znojil, Miloslav
#FOS: Physical sciences #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.quant-ph/0511110
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.