Abstract
A conical closed resonator with perfectly conducting walls is considered. The eigenmodes of the resonator are determined in the first order of perturbation theory, in which the cone angle is a small quantity. A semiclassical approximation is constructed for an arbitrary cone angle; it is shown that the spectrum of whispering gallery modes in this approximation differs insignificantly from the eigenmode spectrum of a cylindrical cavity even for a large cone angle.
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