J.Blaschke and M. Brack

*Quantum corrections to
the semiclassical level density of the circular disk in homogeneous magnetic
fields*

Physica E **1**, 288 (1998)

In the semiclassical trace formula for the level density of a circular
billiard in homogeneous magnetic fields, quantum corrections to the Maslov
phase have shown to be important in strong fields. In this article further
quantum correcions are considered, namely, *grazing corrections*,
which are relevant for whispering-gallery orbits. and a uniform approximation
to the *bifurcation points* in strong fields is applied. Both corrections
are shown to have a surprisingly small effect on the semiclassical level
density. Implementing those corrections requires a technique different
from the common Gaussian smoothing in the numerical evaluation of the trace
formula. The appropiate generalization is presented.