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Title: Self-adjoint extensions for quantum physics
Author: Estévez Estudis, Joan
Director/Tutor: Mas Blesa, Albert
Keywords: Teoria d'operadors
Treballs de fi de grau
Espais de Sobolev
Teoria quàntica
Operator theory
Bachelor's theses
Sobolev spaces
Quantum theory
Issue Date: 29-Jun-2017
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.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2017, Director: Albert Mas Blesa
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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