Pseudo-Hermiticity of Hamiltonians under gauge-like transformation: real spectrum of non-Hermitian Hamiltonians

摘要

We report that it is the pseudo-Hermiticity of Hamiltonians under the gauge-like transformation that underlies the reality of the spectrum and orthogonality of states for the non-Hermitian Hamiltonians type H-beta = [p + ibetanu(x)](2)/2m + V(x), which could be both PT-symmetric and non-PT-symmetric. Notably, the eigenstates of Hp, when it is PT-symmetric, are real and do not satisfy the PT-orthogonality condition. (C) 2002 Elsevier Science B.V. All rights reserved. [References: 25]