Geodesic
The difference equation related to the problem of the hydrogen atom in a strong magnetic field
Electronic transactions on numerical analysis, Tome 27 (2007), pp. 163-176.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We study the Schr$\ddot $odinger equation for the hydrogen atom in an arbitrarily strong magnetic field in two dimensions, which is an integrable and separable system. The energy spectrum is very interesting as it has infinitely many accumulation points located at the values of the Landau energy levels of a free electron in the uniform magnetic field. In the polar coordinates the canonical (not kinetic!) angular momentum has a precise eigenvalue and we have the one dimensional radial Schr$\ddot $odinger equation which is an ordinary second order differential equation whose analytic exact solution is unknown. The problem is reduced to a linear three-term recurrence difference equation whose solution is unknown. We describe the qualitative properties of the energy spectrum and propose a semi-analytic method to numerically calculate the eigenenergies.
Classification : 81V45, 81Q10
Keywords: hydrogen atom, strong magnetic field 
@article{ETNA_2007__27__a0,
     author = {Robnik, Marko and Romanovski, Valery G.},
     title = {The difference equation related to the problem of the hydrogen atom in a strong magnetic field},
     journal = {Electronic transactions on numerical analysis},
     pages = {163--176},
     publisher = {mathdoc},
     volume = {27},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2007__27__a0/}
}
TY  - JOUR
AU  - Robnik, Marko
AU  - Romanovski, Valery G.
TI  - The difference equation related to the problem of the hydrogen atom in a strong magnetic field
JO  - Electronic transactions on numerical analysis
PY  - 2007
SP  - 163
EP  - 176
VL  - 27
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ETNA_2007__27__a0/
LA  - en
ID  - ETNA_2007__27__a0
ER  - 
%0 Journal Article
%A Robnik, Marko
%A Romanovski, Valery G.
%T The difference equation related to the problem of the hydrogen atom in a strong magnetic field
%J Electronic transactions on numerical analysis
%D 2007
%P 163-176
%V 27
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ETNA_2007__27__a0/
%G en
%F ETNA_2007__27__a0
Robnik, Marko; Romanovski, Valery G. The difference equation related to the problem of the hydrogen atom in a strong magnetic field. Electronic transactions on numerical analysis, Tome 27 (2007), pp. 163-176. http://geodesic.mathdoc.fr/item/ETNA_2007__27__a0/