# Bonn 2010 – wissenschaftliches Programm

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# MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

## MP 8: Quantum Mechanics

### MP 8.1: Vortrag

### Mittwoch, 17. März 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*(|*x*_{1}|^{d}+|*x*_{2}|^{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*≤ *d*_{0} where *d*_{0} increases with nuclear charge) increases with a power law *B*^{s} with *s*=1/(2+*d*). This contrasts the logarithmic increase with *B* in the nonrelativistic (*d*=0) case.