The Quantum Kepler Problem

Guillermo Chacón‐Acosta, Héctor H. Hernández

Arno Böhm

Arno Böhm

Guowu Meng

The Kepler problem is a physical problem about two bodies which attract each other by a force proportional to the inverse square of the distance. The MICZ-Kepler problems are its natural cousins and have been previously generalized from dimension 3 to dimension 5. In this paper, we construct and analyze the (quantum) MICZ-Kepler problems in all dimensions higher than 2.

Barry R. Clarke

Piotr Garbaczewski

The stochastic mechanics of Nelson and Guerra is formulated for the hydrogen atom. We demonstrate that this simple quantum system can be described in terms of three independent Gaussian Markov processes which are driven (controlled) by the classical Kepler problem. It reveals a manifest connection between the classical and quantized versions of the Kepler problem.