We study the time-independent Schrodinger equation with radially symmetric potential , , on a bounded domain in , with Dirichlet boundary conditions. In particular, we compare the eigenvalue of the operator on with the eigenvalue of the same operator on a ball , where has radius such that the first eigenvalues are the same, . The main result is to show . We also give an extension of the main result to the case of a more general elliptic eigenvalue problem on a bounded domain with Dirichlet boundary conditions.
Submitted August 24, 1999. Published Janaury 28, 2000.
Math Subject Classifications: 35J10, 35J15, 35J25, 35P15.
Key Words: Schrodinger eigenvalue equation, Dirichlet boundary conditions, eigenvalue bounds, radially symmetric potential.
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| Craig Haile |
Department of Mathematics and Physics
College of the Ozarks
Point Lookout, MO 65726-0017, USA
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