An estimate for solutions to the Schrodinger equation

Abstract

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.

Keywords

• Schrodinger operator
• spectral parameter
• eigenfunction.