Pseudo-Hermiticity of Hamiltonians under gauge-like transformation: real spectrum of non-Hermitian Hamiltonians. (English) Zbl 0990.81029
Summary: 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 \(H_{\beta}=[p+i\beta\nu (x)]^2/2m+V(x)\), which could be both PT-symmetric and non-PT-symmetric. Notably, the eigenstates of \(H_{\beta}\), when it is PT-symmetric, are real and do not satisfy the PT-orthogonality condition.
MSC:
| 81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
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