Bonn 2010 – scientific programme
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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 8: Quantum Mechanics
MP 8.1: Talk
Wednesday, March 17, 2010, 15:00–15:25, JUR H
Pseudorelativistic operators in the limit of strong magnetic fields — •Doris Jakubassa-Amundsen — Math. Institut, LMU München
Relativistic one-electron ions serve as a tool for probing the description of many-electron systems by means of pseudorelativistic operators. The two operators considered are the Chandrasekhar operator which allows for relativistic kinematics in place of the Laplace operator, and the no-pair Brown-Ravenhall operator which results from a projection of the Dirac operator onto the electronic subspace.
When the ions move in a locally bounded magnetic field of the type (0,0,B(|x1|d+|x2|d)) with d≥ 0, both pseudorelativistic operators obey a scaling property which relates an increasing field B to a decreasing particle mass. It is strictly shown that, when B goes to infinity, the binding energy of the ground state (existing as a discrete state for d≤ d0 where d0 increases with nuclear charge) increases with a power law Bs with s=1/(2+d). This contrasts the logarithmic increase with B in the nonrelativistic (d=0) case.