Geometric quantization of the five-dimensional Kepler problem

Vassil V. Tsanov, Ivaïlo M. Mladenov

MICHAEL TRUNK

Starting from the structural similarity between the quantum theory of gauge systems and that of the Kepler problem, an SU(2) gauge description of the five-dimensional Kepler problem is given. This non-Abelian gauge system is used as a testing ground for the application of an algebraic constraint quantization scheme which can be formulated entirely in terms of observable quantities. For the quantum-mechanical reduction, only the quadratic Casimir of the constraint algebra, interpreted as an observable, is needed.

Jędrzej Śniatycki

Guillermo Chacón‐Acosta, Héctor H. Hernández

Bruno Cordani

In Chapter 4 we have quantized the Kepler Problem using the Schrödinger method, i.e., we have found the eigenvalues and the eigenfunctions of the Hermitian operator $$\begin{array}{*{20}{c}} {\hat{H} = \frac{1}{2}{{{\hat{p}}}^{2}} - \frac{1}{q},} & {where} & {{{{\hat{p}}}_{k}} = - i\frac{\partial }{{\partial {{q}^{k}}}}.} \\ \end{array}$$

Norman E. Hurt