# Superintegrable quantum oscillator and Kepler-Coulomb systems on curved spaces

An overview of maximally superintegrable classical Hamitonians on spherically symmetric spaces is presented. It turns out that each of these systems can be considered either as an oscillator or as a Kepler-Coulomb Hamiltonian. We show that two possible quantization prescriptions for all these curved systems arise if we impose that superintegrability is preserved after quantization, and we prove that both possibilities are gauge equivalent.

Article:

Superintegrable quantum oscillator and Kepler-Coulomb systems on curved spaces

Journal:

The XXIX International Colloquium on Group-Theoretical Methods in Physics", August 20-26, 2012, Chern Institute of Mathematics, Tianjin, China. Nankai Series in Pure, Applied Mathematics and Theoretical Physics, Chengming Bai

Year:

2013

URL:

http://arxiv.org/abs/1304.4544