Vector Models in PT Quantum Mechanics
Quantum Physics
2014-07-02 v1
Abstract
We present two examples of non-Hermitian Hamiltonians which consist of an unperturbed part plus a perturbation that behaves like a vector, in the framework of PT quantum mechanics. The first example is a generalization of the recent work by Bender and Kalveks, wherein the E2 algebra was examined; here we consider the E3 algebra representing a particle on a sphere, and identify the critical value of coupling constant which marks the transition from real to imaginary eigenvalues. Next we analyze a model with SO(3) symmetry, and in the process extend the application of the Wigner-Eckart theorem to a non-Hermitian setting.
Cite
@article{arxiv.1304.5692,
title = {Vector Models in PT Quantum Mechanics},
author = {Katherine Jones-Smith and Rudolph Kalveks},
journal= {arXiv preprint arXiv:1304.5692},
year = {2014}
}