Physics – Quantum Physics
Scientific paper
2006-03-03
J. Math. Phys. 47, 072103 (2006)
Physics
Quantum Physics
14 pages, slightly expanded (published) version
Scientific paper
10.1063/1.2212668
For a given pseudo-Hermitian Hamiltonian of the standard form: H=p^2/2m+v(x), we reduce the problem of finding the most general (pseudo-)metric operator \eta satisfying H^\dagger=\eta H \eta^{-1} to the solution of a differential equation. If the configuration space is the real line, this is a Klein-Gordon equation with a nonconstant mass term. We obtain a general series solution of this equation that involves a pair of arbitrary functions. These characterize the arbitrariness in the choice of \eta. We apply our general results to calculate \eta for the PT-symmetric square well, an imaginary scattering potential, and a class of imaginary delta-function potentials. For the first two systems, our method reproduces the known results in a straightforward and extremely efficient manner. For all these systems we obtain the most general \eta up to second order terms in the coupling constants.
No associations
LandOfFree
Differential Realization of Pseudo-Hermiticity: A quantum mechanical analog of Einstein's field equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Differential Realization of Pseudo-Hermiticity: A quantum mechanical analog of Einstein's field equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Differential Realization of Pseudo-Hermiticity: A quantum mechanical analog of Einstein's field equation will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-118820