Quantum Chaos On A Curved Surface

Abstract: The system studied in the thesis is a particle in a two-dimensional box on the surface of a sphere with constant radius. The different systems have different radii while the box dimension is kept the same, so the curvature of the surface of the box is different for the different systems. In a system with a sphere of a large radius the surface of the box is almost flat. What happens if the radius is decreased and the symmetry is broken? Will the system become chaotic if the radius is small enough? There are some properties of the eigenfunctions, that show different things depending on whether the system is chaotic or regular. The  amplitude distribution of the probability density, the amplitude distribution of the eigenfunction and the probability density look different for chaotic and regular systems. The main subject of this thesis is to study these distributions.