PT-Rotations, PT-Spherical Harmonics and the PT-Hydrogen Atom
Abstract
We have constructed a set of non-Hermitian operators that satisfy the commutation relations of the SO(3)-Lie algebra. It is shown that this operators generate rotations in the configuration space and not in the momentum space but in a modified non-Hermitian momentum space. This generators are related with a new type of spherical harmonics that result to be PT-orthonormal. Additionally, we have shown that this operators represent conserved quantities for a non-Hermitian Hamiltonian with an additional complex term. As a particular case, the solutions of the corresponding PT-Hydrogen atom that includes a complex term are obtained, and it is found that a non-Hermitian Runge-Lenz vector is a conserved quantity. In this way, we obtain a set of non-Hermitian operators that satisfy the SO(4)-Lie algebra.
Keywords
Cite
@article{arxiv.1001.1579,
title = {PT-Rotations, PT-Spherical Harmonics and the PT-Hydrogen Atom},
author = {Juan M. Romero and R. Bernal-Jaquez and O. Gonzalez-Gaxiola},
journal= {arXiv preprint arXiv:1001.1579},
year = {2010}
}
Comments
10 pages, no figures