Optimal Potentials For Schrodinger Operators

TL;DR

This paper investigates optimization problems for Schrödinger operators, focusing on determining optimal non-negative potentials within specific classes to optimize criteria like energy or eigenvalues.

Contribution

It introduces new methods for identifying optimal potentials in Schrödinger operators under various criteria and admissible classes.

Findings

Characterization of optimal potentials for energy minimization.

Results on eigenvalue optimization for Schrödinger operators.

Development of a framework for potential optimization in quantum systems.

Abstract

We consider the Schrodinger operator a given domain. Our goal is to study some optimization problems where an optimal (non-negative) potential V has to be determined in some suitable admissible classes and for some suitable optimization criteria, like the energy or the Dirichlet eigenvalues.