On a stationary Schr{\"o}dinger equation with periodic magnetic potential

TL;DR

This paper proves the existence of solutions for a stationary Schrödinger equation with a periodic magnetic potential, expanding understanding of quantum systems with magnetic fields.

Contribution

It introduces a new approach using a critical value function to establish existence results under local integrability conditions.

Findings

Existence of solutions under periodic magnetic potentials.

Application of critical value function method.

Results applicable to quantum systems with magnetic fields.

Abstract

We prove existence results for a stationary Schr{\"o}dinger equation with periodic magnetic potential satisfying a local integrability condition on the whole space using a critical value function.