Eigenvalues of Schrödinger operators on finite and infinite intervals

Abstract

AbstractWe consider a Sturm–Liouville operator with an integrable potential q on the unit interval . We consider a Schrödinger 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.