Semiclassical expansion of the smooth part of the density of states, with application to the hydrogen atom in a uniform magnetic field.
We present a method to compute the smooth part of the density of states in a semiclassical expansion when the Hamiltonian contains a Coulomb potential and non-Cartesian coordinates are appropriate. We apply this method to the case of the hydrogen atom in a magnetic field with fixed z component of the angular momentum. This is then compared with numerical results obtained by a high precision finite element approach. The agreement is excellent, especially in the chaotic region of the spectrum. The need to go beyond the Thomas-Fermi model is clearly established.
Institute of Theoretical Physics, Swiss Federal Institute of Technology EPFL, Station 3, CH-1015 Lausanne, Switzerland. herve.kunz@epfl.ch
Hervé
H
Kunz
Thierry
T
Schüpbach
Marc-André
MA
Dupertuis