Pseudo-Hermiticity for a class of nondiagonalizable Hamiltonians
Pseudo-Hermiticity for a class of nondiagonalizable Hamiltonians
We give two characterization theorems for pseudo-Hermitian (possibly nondiagonalizable) Hamiltonians with a discrete spectrum that admit a block-diagonalization with finite-dimensional diagonal blocks. In particular, we prove that for such an operator H the following statements are equivalent. 1. H is pseudo-Hermitian; 2. The spectrum of H consists of real and/or …