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The Fundamental Gap for a Class of Schrodinger Operators on Path and Hypercube Graphs

Published

Author(s)

Stephen P. Jordan

Abstract

We consider the difference between the two lowest eigenvalues (the fundamental gap) of a Schrodinger operator acting on a class of graph Laplacians. In particular, we derive tight bounds for the set of convex potentials acting on the path and hypercube graphs. Our proof begins by simplifying the problem with variational techniques. We then make extensive use of the Hellman-Feynman theorem, the recurrence relations on the first two eigenvectors, and techniques specific to the discrete space to complete the proof. We prove the tight bound for the hypercube graph as a corollary to our path graph results.
Citation
Journal of Mathematical Physics
Volume
55
Issue
5

Keywords

quantum, spectral gap, eigenvalues, graph

Citation

Jordan, S. (2014), The Fundamental Gap for a Class of Schrodinger Operators on Path and Hypercube Graphs, Journal of Mathematical Physics (Accessed February 25, 2024)
Created May 29, 2014, Updated February 19, 2017