Hydrogen atom in phase space: The Kirkwood-Rihaczek representation

The two-dimensional hydrogen atom in The momentum representation

The analytic expression of the momentum representation in terms of the associated Legendre function is determined by a direct integration of Fourier transform of the wave function of coordinates using the Levi-Civita transformation and 2 2 R R → the generating function method. A new generating function for the associated Legendre functions are obtained.

1 On the N - dimensional hydrogen atom in momentum representation

We derive the wave function for N-dimensional hydrogen atom in the momentum representation with the phase factor using the generating function method and Hankel’s integral.

Phase space structure of the hydrogen atom in a circularly polarized microwave field

We consider the problem of the hydrogen atom interacting with a circularly polarized microwave field, modeled as a perturbed Kepler problem. A remarkable feature of this system is that the electron can follow what we term erratic orbits before ionizing. In an erratic orbit the electron makes multiple large distance excursions from the nucleus with each excursion being followed by a close approa...

Canonical partition function for the hydrogen atom in curved space

The electronic partition function for the hydrogen atom was recently derived by integration over the Coulomb propagator. A much simpler derivation is given here, based on Schrfdinger's exact solution for a hydrogenic atom in a Riemannian space of positive curvature. The energy spectrum is entirely discrete, including states which correspond to the ionized atom. The curvature in Riemannian space...

Phase space structures and ionization dynamics of hydrogen atom in elliptically polarized microwaves