Lower bounds on the spectral gap of one-dimensional Schrödinger operators

DOI10.1007/s00013-022-01786-2OpenAlexW4304688913MaRDI QIDQ2099112

Joachim Kerner

Publication date: 23 November 2022

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00013-022-01786-2

zbMATH Keywords

eigenvaluesSchrödinger operatorsspectral gap

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Spectrum, resolvent (47A10) General theory of ordinary differential operators (47E05) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15)

Cites Work

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• Universal lower bounds on eigenvalue splittings for one dimensional Schrödinger operators
• Comparison theorems for the gap of Schrödinger operators
• Optimal Lower Bound for the Gap Between the First Two Eigenvalues of One-Dimensional Schrodinger Operators with Symmetric Single-Well Potentials
• The Eigenvalue Gap for One-Dimensional Convex Potentials
• Spectral gaps of 1-D Robin Schrödinger operators with single-well potentials
• A Harnack Inequality for Ordinary Differential Equations
• The Gap between the First Two Eigenvalues of a One-Dimensional Schrodinger Operator with Symmetric Potential
• The fundamental gap for a one-dimensional Schrödinger operator with Robin boundary conditions
• On the spectral gap of higher-dimensional Schrödinger operators on large domains

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