Hydrogen Atom—The Quantum-Mechanical Kepler Problem

Arno Böhm

V. K. Gudym, E. V. Andreeva

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.

Bogdan Povh, Mitja Rosina

José M. Gracia-Bondı́a

Using a coordinate transformation which regularizes the classical Kepler problem, we show that the hydrogen-atom case may be analytically solved via the phase-space formulation of nonrelativistic quantum mechanics. The problem is essentially reduced to that of a four-dimensional oscillator whose treatment in the phase-space formulation is developed. Furthermore, the method allows us to calculate the Green's function for the H atom in a surprisingly simple way.