On the calculation of exact sum rules of rational order for quantum billiards
Mathematical Physics
2019-08-26 v1 math.MP
Abstract
We study the Helmholtz equation for a heterogeneous system in dimensions and show that it is possible to calculate exactly the sum rules of rational order using perturbation theory by relating the sum rules to suitable traces. The present calculation is restricted to a positive definite spectrum, e.g. Dirichlet boundary conditions, and it reproduces the result previously obtained in Ref.~\cite{Amore12}, working directly with Rayleigh-Schr\"odinger perturbation theory.
Keywords
Cite
@article{arxiv.1908.08561,
title = {On the calculation of exact sum rules of rational order for quantum billiards},
author = {Paolo Amore},
journal= {arXiv preprint arXiv:1908.08561},
year = {2019}
}
Comments
13 pages