Dynamics of some bouncing ball systems

Motion of a particle in the two-dimensional lemon shaped billiard is investigated both classically and quantally. Poincare sections, periodic orbits and the wave functions are presented for selected cases. Level density fluctuations are calculated using NNSD method. Chaotic and regular classical motion of the Fermi oscillator, consisting of mass M supported by a spring with constant k and a particle of mass m falling freely and colliding with mass M, is analysed.