# name
The Schrödinger equation and chaotic dynamics

# metadata.dc.description[].value
Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2022, Director: Marina Gonchenko

# metadata.dc.description.abstract[].value
[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.

# metadata.dc.rights[].value
cc-by-nc-nd (c) Marta Botella Garcia, 2022

# metadata.dc.source[].value
Treballs Finals de Grau (TFG) - Matemàtiques

# metadata.dc.title[].value
The Schrödinger equation and chaotic dynamics