Electron. J. Diff. Eqns., Vol. 2004(2004), No. 34, pp. 1-8.

An estimate for solutions to the Schrodinger equation

Alexander Makin & Bevan Thompson

In this note, we find a priori estimates in the $L_2$-norm for solutions to the Schrodinger equation with a parameter. It is shown that a constant occuring in the inequality does not depend on the value of the parameter. In particular, the estimate is valid for eigenfunctions associated with the Schrodinger operator with arbitrary boundary conditions.

Submitted May 29, 2003. Published March 10, 2004.
Math Subject Classifications: 35B45, 35J10.
Key Words: Schrodinger operator, spectral parameter, eigenfunction.

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Alexander Makin
Moscow State Academy of Instrument-Making and Informatics
Stromynka 20, 107846, Moscow, Russia
email: alexmakin@yandex.ru
Bevan Thompson
Department of Mathematics, The University of Queensland
Brisbane Qld 4072 Australia
email: hbt@maths.uq.edu.au

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