
Helmholtz EquationThe group of the physicist Prof. Dr. A. Richter uses experiments with microwaves to study quantum manifestation of classical chaos. To this end, they build superconductive microwave resonators and measure the spectrum of eigenvalues. For details click here. As an example the following picture shows a flat resonator for a Pascalian snail: The physical experiment is mathematically described by the stationary Helmholtz equation: The finite element discretisation of this equation leads to a generalised eigenvalue problem:
Using WebSplines of degree 5 on a 75x75 grid we are able to compute 2000 eigenvalues with relative error less then 10^{4} in half an hour on a 2 GHz standard PC . Here are some examples of the corresponding eigenfunctions: first eigenfunction, k^{2} = 106.6774
tenth eigenfunction, k^{2} = 960.0726 fiftieth eigenfunction, k^{2} = 4119.0409 LiteratureA. Richter: Playing Billiards with Microwaves  Quantum Manifestations of Classical Chaos, The IMA Volumes in Mathematics and its Application, Vol. 109, Springer 1999.See Publications for a complete list of WEBpublications.
Author: Bernhard Mößner ; Last modification: 2003/10/17 16:17:04 UTC.
