Gonchenko, MarinaBotella Garcia, Marta2022-09-072022-09-072022-06-13https://hdl.handle.net/2445/188765Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: Marina Gonchenko[en] This work explores dynamical billiards and its general properties and focuses, in particular, in the Bunimovich stadium which is one of the most studied among known chaotic billiards. This project follows with the analytical resolution of the time independent Schrödinger equation for the case of the simple harmonic oscillator potential. It is also solved numerically for the one-dimensional and two-dimensional cases, developing a Matlab programming that uses the finitedifferences method with the aim to find the eigenvalues and eigenfunctions. Finally, the union of chaotic dynamics and quantum mechanics is explored to investigate quantum chaos and one of its most striking manifestations, quantum "‘scars"’. The numerical analysis is able to replicate the evidence of scarring for the Bunimovich stadium.51 p.application/pdfengcc-by-nc-nd (c) Marta Botella Garcia, 2022http://creativecommons.org/licenses/by-nc-nd/3.0/es/Operadors diferencialsTreballs de fi de grauSistemes dinàmics diferenciablesAnàlisi numèricaTeoria quànticaEquació de SchrödingerDifferential operatorsBachelor's thesesDifferentiable dynamical systemsNumerical analysisQuantum theorySchrödinger equationinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess