Files

memoria.pdf (235.18 KB)

Document type

Bachelor thesis

Publication date

2017-06-29

Publication license

cc-by-nc-nd (c) Joan Estévez Estudis, 2017
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/121893

Self-adjoint extensions for quantum physics

Journal Title

Authors

Director/Tutor

Journal ISSN

Volume Title

Related resource

Abstract

[en] The main goal of this work is to provide techniques for finding self-adjoint extensions to unbounded operators, widely used in Quantum Physics. For that we use and study the Cayley method, concluding in the existance of a bijection between self-adjoint extensions and isometries between the deficiency subspaces of the Cayley transform. Using this knowledge we briefly parameterise the 1D, 2D and nD cases with possible self-adjoint extensions, and after introducing Sobolev spaces, we perform in more detail the search of self-adjoint extensions of the hamiltonian and laplacian operators.

Description

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2017, Director: Albert Mas Blesa

Subject

Teoria d'operadors, Treballs de fi de grau, Espais de Sobolev, Teoria quàntica

Subject (English)

Operator theory, Bachelor's theses, Sobolev spaces, Quantum theory

Citation

Collections

Treballs Finals de Grau (TFG) - Matemàtiques

Citation

ESTÉVEZ ESTUDIS, Joan. Self-adjoint extensions for quantum physics. [consulted: 16 of June of 2026]. Available at: https://hdl.handle.net/2445/121893

Export metadata

JSON - METS

Share record