Exact sum rules for inhomogeneous drums

Journal Article · Sun Sep 15 04:00:00 EDT 2013 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/J.AOP.2013.05.010· OSTI ID:22220779

Amore, Paolo

We derive general expressions for the sum rules of the eigenvalues of drums of arbitrary shape and arbitrary density, obeying different boundary conditions. The formulas that we present are a generalization of the analogous formulas for one dimensional inhomogeneous systems that we have obtained in a previous paper. We also discuss the extension of these formulas to higher dimensions. We show that in the special case of a density depending only on one variable the sum rules of any integer order can be expressed in terms of a single series. As an application of our result we derive exact sum rules for the homogeneous circular annulus with different boundary conditions, for a homogeneous circular sector and for a radially inhomogeneous circular annulus with Dirichlet boundary conditions. -- Highlights: •We derive an explicit expression for the sum rules of inhomogeneous drums. •We discuss the extension to higher dimensions. •We discuss the special case of an inhomogeneity only along one direction.

• OSTI ID: 22220779
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Vol. 336; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY CONDITIONS
DIRICHLET PROBLEM
EIGENVALUES
SUM RULES