Notes on free fall of a particle and bouncing on a reflecting surface

Considerable progress has recently been made in controling the motion of free atomic particles by means of light pressure exerted by laser radiation. The free fall of atoms and bouncing on a reflecting surface made from evanescent wave formed by internal reflection of a quasiresonant laser beam at a curved glass surface in the presence of homogeneous gravitational field has been observed. In this paper we present the energy quantization of this system by making use the asymptotic expansion method. It is shown that for large $n$ the levels go like $n^{2/3}$ which may be compared with $n^2$ for the infinite square well.