An alternative construction of the positive inner product for pseudo-Hermitian Hamiltonians: Examples

作者：Das Ashok^*; Greenwood L

来源：Journal of Mathematical Physics, 2010, 51(4): 042103.

DOI：10.1063/1.3373551

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 x 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).

• 出版日期2010-4