Quantization of a Particle on a Two-Dimensional Manifold of Constant Curvature
Mathematical Physics
2015-06-22 v1 math.MP
Quantum Physics
Abstract
The formulation of quantum mechanics on spaces of constant curvature is studied. It is shown how a transition from a classical system to the quantum case can be accomplished by the quantization of the Noether momenta. These can be determined by Lie differentiation of the metric which defines the manifold. For the metric examined here, it is found that the resulting Schrodinger equation is separable and the spectrum and eigenfunctions can be investigated in detail.
Keywords
Cite
@article{arxiv.1407.0734,
title = {Quantization of a Particle on a Two-Dimensional Manifold of Constant Curvature},
author = {Paul Bracken},
journal= {arXiv preprint arXiv:1407.0734},
year = {2015}
}