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tfg_botella_garcia_marta.pdf (1.26 MB)

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Bachelor thesis

Publication date

2022-06-13

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cc-by-nc-nd (c) Marta Botella Garcia, 2022
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/188765

The Schrödinger equation and chaotic dynamics

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Abstract

[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.

Description

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: Marina Gonchenko

Subject

Operadors diferencials, Treballs de fi de grau, Sistemes dinàmics diferenciables, Anàlisi numèrica, Teoria quàntica, Equació de Schrödinger

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Differential operators, Bachelor's theses, Differentiable dynamical systems, Numerical analysis, Quantum theory, Schrödinger equation

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Treballs Finals de Grau (TFG) - Matemàtiques

Citation

BOTELLA GARCIA, Marta. The Schrödinger equation and chaotic dynamics. [consulted: 18 of June of 2026]. Available at: https://hdl.handle.net/2445/188765

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