On minimal and maximal eigenvalue gaps and their causes

Mark S. Ashbaugh, Evans Malott Harrell, II and Roman Svirsky

Vol. 147 (1991), No. 1, 1–24

DOI: 10.2140/pjm.1991.147.1

Abstract

We consider quantum-mechanical potentials giving rise to minimal (or maximal) eigenvalue gaps subject to L^P constraints in n-dimensions. We prove existence and characterization theorems for optimizing potentials. The tunneling effect through a single barrier is shown always to be the cause of minimal gaps, and in some cases the gap minimizers are shown to be specific double-well potentials.

Mathematical Subject Classification 2000

Primary: 35P15

Secondary: 35J10, 81Q10

Milestones

Received: 28 December 1988

Revised: 3 July 1989

Published: 1 January 1991