# Eigenvalues of Schr\"odinger operators on finite and infinite intervals

Research paper by Evgeny Korotyaev

Indexed on: 05 Sep '18Published on: 05 Sep '18Published in: arXiv - Mathematics - Spectral Theory

#### Abstract

We consider a Sturm-Liouville operator a with integrable potential \$q\$ on the unit interval \$I=[0,1]\$. We consider a Schr\"odinger operator with a real compactly supported potential on the half line and on the line, where this potential coincides with \$q\$ on the unit interval and vanishes outside \$I\$. We determine the relationships between eigenvalues of such operators and obtain estimates of eigenvalues in terms of potentials.