| In this thesis we present the solution to two scientific problems.; First, we consider the quantum treatment of triangular billiards. We present an original computation scheme for the eigenvalues and eigenfunctions of triangular billiards, and we assess the precision and reliability of the method by comparison with some analytical results. We then study the statistical properties of the spectra of some representative billiards, and observe the weak dependence of such properties on the {dollar}rm{lcub}setminus em{dollar} genus) of the invariant, classical phase space hypersurface. Finally, we discover a new phenomenon, namely scars along neutrally stable periodic orbits, and also along ghosts of such orbits, and we give quantitative evidence of the scarring of the eigenfunctions.; Second, we solve the problem of the excitation of large angular momentum Rydberg states, by slow collisions with ions. We identify analytically, for a purely hydrogenic model, the conditions under which transitions to large angular momentum states are to be expected and we show that under typical experimental conditions such transitions are statistically favored. We then extend the model to alkali Rydberg atoms; we accurately reproduce several experimental results and also confirm the hydrogenic results for the excitation of large angular momenta. |
