In this paper, we build on our earlier proposal for the construction of a positive inner product for pseudo-Hermitian Hamiltonians and present examples to clarify the procedure. We focus on two detailed calculations where the method is used, namely, a simple (generalized 2×2 matrix) pseudo-Hermitian Hamiltonian, which can be diagonalized, and a second system where the Hamiltonian cannot be diagonalized, but can be described as a perturbation of the harmonic oscillator. When the quantum mechanical system cannot be diagonalized exactly, our construction can be carried out perturbatively and we develop the general formalism for such a perturbative calculation systematically (for real eigenvalues).In this paper, we build on our earlier proposal for the construction of a positive inner product for pseudo-Hermitian Hamiltonians and present examples to clarify the procedure. We focus on two detailed calculations where the method is used, namely, a simple (generalized 2×2 matrix) pseudo-Hermitian Hamiltonian, which can be diagonalized, and a second system where the Hamiltonian cannot be diagonalized, but can be described as a perturbation of the harmonic oscillator. When the quantum mechanical system cannot be diagonalized exactly, our construction can be carried out perturbatively and we develop the general formalism for such a perturbative calculation systematically (for real eigenvalues).

arXiv:0912.1678Journal of Mathematical PhysicsApr 1, 201021 citations

Pseudo-Hermitian Hamiltonians: tale of two potentials

Hugh F Jones, J. Mateo

Czechoslovak Journal of PhysicsSep 1, 200513 citations

On Pseudo-Hermitian Hamiltonians

Soumendu Sundar Mukherjee, Pinaki Roy

We investigate some questions on the construction of $η$ operators for pseudo-Hermitian Hamiltonians. We give a sufficient condition which can be exploited to systematically generate a sequence of $η$ operators starting from a known one, thereby proving the non-uniqueness of $η$ for a particular pseudo-Hermitian Hamiltonian. We also study perturbed Hamiltonians for which $η$ 's corresponding to the original Hamiltonian still work.We investigate some questions on the construction of $η$ operators for pseudo-Hermitian Hamiltonians. We give a sufficient condition which can be exploited to systematically generate a sequence of $η$ operators starting from a known one, thereby proving the non-uniqueness of $η$ for a particular pseudo-Hermitian Hamiltonian. We also study perturbed Hamiltonians for which $η$'s corresponding to the original Hamiltonian still work.

arXiv:1401.5255Jan 21, 20141 citation

On the pseudo-Hermitian nondiagonalizable Hamiltonians

G. Scolarici, Luigi Solombrino

Jan 1, 20030 citations

We investigate some questions on the construction of

η

operators for pseudo-Hermitian Hamiltonians. We give a sufficient condition which can be exploited to systematically generate a sequence of

η

operators starting from a known one, thereby proving the non-uniqueness of

η

for a particular pseudo-Hermitian Hamiltonian. We also study perturbed Hamiltonians for which

η

's corresponding to the original Hamiltonian still work.