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2011, 2011(Special): 1309-1318. doi: 10.3934/proc.2011.2011.1309

Superradiance problem in a 3D annular domain

Indranil SenGupta 1, , Weisheng Jiang 2, , Bo Sun 3, and  Maria Christina Mariani 1,

1. 

Department of Mathematical Sciences, The University of Texas- El Paso, El Paso, Texas 79968-0514, United States, United States
2. 

College of Mathematics and Statistics, Chongqing University, Chongqing 400044, China
3. 

College of Mathematics and Computers, Changsha University of Science and Technology, Changsha, Hu'nan 410076, China

Received  July 2010 Revised  April 2011 Published  October 2011

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.
Keywords: Sturm-Liouville problem, Quantum optics, Spherical harmonics, Dy- namical systems.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.
Citation: Indranil SenGupta, Weisheng Jiang, Bo Sun, Maria Christina Mariani. Superradiance problem in a 3D annular domain. Conference Publications, 2011, 2011 (Special) : 1309-1318. doi: 10.3934/proc.2011.2011.1309
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