Symmetric Potentials Beget Symmetric Ground States

TL;DR

This paper demonstrates that for various equations with symmetric potentials, the ground state, if it exists, must also be symmetric, using a novel symmetric averaging method.

Contribution

Introduces a new symmetric averaging technique to prove symmetry of ground states in equations with symmetric potentials.

Findings

Ground states are symmetric when potentials are symmetric.

The method applies to several common equations.

Symmetry of ground states is guaranteed under broad conditions.

Abstract

Using an unusual type of symmetric average, we show that for several common equations involving quite general potentials possessing symmetry, the ground state, if it exists, must also be symmetric.