Convexity and concavity of the ground state energy

TL;DR

This paper proves that the ground state energy of one-dimensional Schrödinger operators exhibits convexity or concavity depending on the nature of the potential, with respect to the interval endpoint.

Contribution

It establishes the convexity and concavity properties of the ground state energy as a function of the interval endpoint for convex and concave potentials, respectively.

Findings

Ground state energy is convex for convex potentials.

Ground state energy is concave for concave potentials.

Results apply to one-dimensional Schrödinger operators.

Abstract

This note proves convexity resp. concavity of the ground state energy of one dimensional Schr\"odinger operators as a function of an endpoint of the interval for convex resp. concave potentials.