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.
Show me the PDF file (194K), TEX file, and other files for this article.
![]() |
Craig Haile Department of Mathematics and Physics College of the Ozarks Point Lookout, MO 65726-0017, USA e-mail: haile@cofo.edu |
Return to the EJDE web page