## The fundamental gap for a one-dimensional Schrödinger operator with Robin boundary conditions

### Ben Andrews, Julie Clutterbuck, Daniel Hauer

#### Abstract

For Schrödinger operators on an interval with either convex or symmetric, single-well potentials, and Robin or Neumann boundary conditions, the gap between the two lowest eigenvalues is minimised when the potential is constant. We also have results for the $$p$$-Laplacian.

Keywords: Eigenvalue problem, Robin boundary condition, fundamental gap, p-Laplacian.

: Primary 47A75; secondary 34B09, 34B15, 34L15, 34L40.

This paper is available as a pdf (236kB) file. It is also on the arXiv: arxiv.org/abs/2002.06900.

 Tuesday, March 24, 2020