Progress in Weyl`s Problem Achieved by Computational Methods

H. P. Baltes
Eberhard R. Hilf   Phone: +49-(0)441-798-2542   Fax: +49-(0)441-798-3201

Files: (Published) (Preprint)

Date: 1972

Article: published in Computer Physics Communications, Vol. 4, p. 208-213, ( 1972 )

The smoothed eigenvalue distribution for the scalar, and the electromagnetic vector,
wave equations are studied for large, but finite wavenumbers k by counting the first
10^6 eigenvalues for various shapes of the domain. The results have implications on
the Fermi-gas model of nuclear matter, the electron gas as well as the long-wave 
acoustic vibration modes in small crystals, the laws of black-body radiation, the
acoustics of complicated resonators, and the thermodynamics of perfect gases in a
finite volume. The relevance of the computational procedure is compared to that of the 
analytical methods yielding asymptotic expansions for the eigenvalue distribution 
which are valid in the limit of infinite k. As an illustrative example for the 
computational procedure, we present the calculation of the electromagnetic mode
density in a lossless cavity with resonator with the shape of a circular cylinder. 
This calculation comprehends the computation of the first 10^4 zeros of the Bessel

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Metadata by Thomas Severiens on 13 April 1999
Supporting work done by Sandra Valeska Bergmann.