Spherical-separablility of non-Hermitian Hamiltonians and pseudo-PT-symmetry
Abstract
Non-Hermitian but P(phi)T(phi)-symmetrized spherically-separable Dirac and Schrodinger Hamiltonians are considered. It is observed that the descendant Hamiltonians H(r), H(theta), and H(phi) play essential roles and offer some "user-feriendly" options as to which one (or ones) of them is (or are) non-Hermitian. Considering a P(phi)T(phi)-symmetrized H(phi), we have shown that the conventional Dirac (relativistic) and Schrodinger (non-relativistic) energy eigenvalues are recoverable. We have also witnessed an unavoidable change in the azimuthal part of the general wavefunction. Moreover, setting a possible interaction V(theta) in the descendant Hamiltonian H(theta) would manifest a change in the angular theta-dependent part of the general solution too. Whilst some P(phi)T(phi)-symmetrized H(phi) Hamiltonians are considered, a recipe to keep the regular magnetic quantum number m, as defined in the regular traditional Hermitian settings, is suggested. Hamiltonians possess properties similar to the PT-symmetric ones (here the non-Hermitian P(phi)T(phi)-symmetric Hamiltonians) are nicknamed as pseudo-PT-symmetric.
Keywords
Cite
@article{arxiv.0801.3572,
title = {Spherical-separablility of non-Hermitian Hamiltonians and pseudo-PT-symmetry},
author = {Omar Mustafa and S. Habib Mazharimousavi},
journal= {arXiv preprint arXiv:0801.3572},
year = {2009}
}
Comments
13 pages, 2 figures. This article is a combination of arXiv:0711.3887 and arXiv:0710.5814