Electron. J. Diff. Eqns., Vol. 2000(2000), No. 10, pp. 1-19.

### A second eigenvalue bound for the Dirichlet Schrodinger equation wtih a radially symmetric potential Craig Haile

Abstract:
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 e-mail: haile@cofo.edu