Bound states in two spatial dimensions in the non-central case

Details Bound states in two spatial dimensions in the non-central case Bound states in two spatial dimensions in the non-central case

2003-10-17

arxiv.org/abs/math-ph/0310035v1

J.Math.Phys. 45 (2004) 922-931

Physics

Mathematical Physics

Work supported in part by the U.S. Department of Energy under Grant No. DE-FG02-84-ER40158

Scientific paper

We derive a bound on the total number of negative energy bound states in a potential in two spatial dimensions by using an adaptation of the Schwinger method to derive the Birman-Schwinger bound in three dimensions. Specifically, counting the number of bound states in a potential gV for g=1 is replaced by counting the number of g_i's for which zero energy bound states exist, and then the kernel of the integral equation for the zero-energy wave functon is symmetrized. One of the keys of the solution is the replacement of an inhomogeneous integral equation by a homogeneous integral equation.

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