Superradiance problem in a 3D annular domain

Indranil SenGupta; Weisheng Jiang; Bo Sun; Maria Christina Mariani

doi:10.3934/proc.2011.2011.1309

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2011, Volume 2011: 1309-1318. Doi: 10.3934/proc.2011.2011.1309 open access

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Superradiance problem in a 3D annular domain

1.
Department of Mathematical Sciences, The University of Texas- El Paso, El Paso, Texas 79968-0514
2.
College of Mathematics and Statistics, Chongqing University, Chongqing 400044
3.
College of Mathematics and Computers, Changsha University of Science and Technology, Changsha, Hu'nan 410076

Received: July 2010

Revised: April 2011

Published: August 2017

Abstract / Introduction Related Papers Cited by

Abstract

Superradiance is an important phenomena in quantum mechanics which has many practical applications. Recently the superradiance integral equation in three-dimensional balls has been extensively studied. In this paper we consider the superradiance integral equation over an annulus. A differential operator that commutes with the radial part of the superradiance integral equation is found. A complete orthogonal basis for the problem is derived. A generalization is given for the problem.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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