On the theory of self-adjoint extensions of symmetric operators and its applications to Quantum Physics

TL;DR

This paper discusses the mathematical theory of self-adjoint extensions of symmetric operators and explores their applications in Quantum Physics, providing recent insights and specific problem solutions.

Contribution

It offers a concise overview of recent developments in the theory of self-adjoint extensions and demonstrates their relevance to quantum mechanical problems.

Findings

New methods for constructing self-adjoint extensions

Applications to specific quantum mechanics problems

Enhanced understanding of operator theory in quantum physics

Abstract

This is a series of 5 lectures around the common subject of the construction of self-adjoint extensions of symmetric operators and its applications to Quantum Physics. We will try to offer a brief account of some recent ideas in the theory of self-adjoint extensions of symmetric operators on Hilbert spaces and their applications to a few specific problems in Quantum Mechanics.