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arXiv · 1908.08561

On the calculation of exact sum rules of rational order for quantum billiards

Paolo Amore
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Abstract

We study the Helmholtz equation for a heterogeneous system in $d$ 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-Schrödinger perturbation theory.

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Paolo Amore. 2019-08-22. On the calculation of exact sum rules of rational order for quantum billiards. https://arxiv.org/abs/1908.08561

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