Quantization of a particle on a twodimensional manifold of constant curvature
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 means of Lie differentiation of the metric which defines the manifold. For the metric examined here, it is found that the resulting Schrödinger equation is separable and the spectrum and eigenfunctions can be investigated in detail.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 October 2014
 DOI:
 10.1063/1.4896817
 arXiv:
 arXiv:1407.0734
 Bibcode:
 2014JMP....55j2102B
 Keywords:

 Mathematical Physics;
 Quantum Physics
 EPrint:
 doi:10.1063/1.4896817