We investigate the quantum effects, in particular the Landau-level quantiza
tion, in the scattering of a particle, the nonadiabatic classical dynamics
of which is governed by an adiabatic invariant. As a relevant example, we s
tudy the scattering of a drifting particle on a magnetic barrier in the qua
ntum limit where the cyclotron energy is much larger than a broadening of t
he Landau levels induced by the nonadiabatic transitions. We find that, des
pite the level quantization, the exponential suppression exp [-2 pid/delta]
(barrier width d, orbital shift per cyclotron revolution delta) of the roo
t-mean-square transverse displacement experienced by the particle after the
scattering is the same in the quantum and the classical regime.