Representations and the Hydrogen Atom

Tasko P. Grozdanov, Е. А. Соловьев

Ludmiła Praxmeyer, K. Wódkiewicz

We present a phase-space representation of the hydrogen atom using the Kirkwood-Rikaczek distribution function. This distribution allows us to obtain analytical results, which is unique because an exact analytical form of the Wigner functions corresponding to the atom states is not known. We show how the Kirkwood-Rihaczek distribution reflects the properties of the hydrogen atom wave functions in the position and momentum representations.

Randell L Mills

Ludmiła Praxmeyer, Jan Mostowski, Krzysztof Wódkiewicz

The hydrogen atom is a fundamental exactly soluble system for which the Wigner function, being a quantum analogue of the joint probability distribution of position and momentum, is unknown. In this paper, we present an effective method of calculating the Wigner function, for all bound states of the nonrelativistic hydrogen atom. The formal similarity between the eigenfunctions of the nonrelativistic hydrogen atom in the momentum representation and the Klein–Gordon propagator has allowed the calculation of the Wigner function for an arbitrary bound state of the hydrogen atom, using a simple atomic integral as a generator. These Wigner functions for some low-lying states are depicted and discussed.

Yurii L. Sokolov

J. Michael Hollas