Mas Blesa, AlbertEstévez Estudis, Joan2018-04-262018-04-262017-06-29https://hdl.handle.net/2445/121893Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2017, Director: Albert Mas Blesa[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.31 p.application/pdfengcc-by-nc-nd (c) Joan Estévez Estudis, 2017http://creativecommons.org/licenses/by-nc-nd/3.0/esTeoria d'operadorsTreballs de fi de grauEspais de SobolevTeoria quànticaOperator theoryBachelor's thesesSobolev spacesQuantum theoryinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess