Eigenvalues of Schrödinger operators on finite and infinite intervals

We consider a Sturm-Liouville operator a with integrable potential $q$ on the unit interval $I=[0,1]$. 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.

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