Eigenvalues of Schrödinger operators on finite and infinite intervals

2018/09/05 by Evgeny Korotyaev, Korotyaev, Evgeny
Mathematics · #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1809.01371

openalex publication_date 2018/09/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

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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