PseudoHermiticity for a class of nondiagonalizable Hamiltonians
Jul, 200211 pages
Published in:
- J.Math.Phys. 43 (2002) 6343-6352,
- J.Math.Phys. 44 (2003) 943 (erratum)
e-Print:
- math-ph/0207009 [math-ph]
DOI:
View in:
Citations per year
Abstract:
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 complex-conjugate pairs of eigenvalues and the geometric multiplicity and the dimension of the diagonal blocks for the complex-conjugate eigenvalues are identical: 3. H is Hermitian with respect to a positive-semidefinite inner product. We further discuss the relevance of our findings for the merging of a complex-conjugate pair of eigenvalues of diagonalizable pseudo-Hermitian Hamiltonians in general, and the PT-symmetric Hamiltonians and the effective Hamiltonian for a certain closed FRW minisuperspace quantum cosmological model in particular.References(18)
Figures(0)