  Consider the quantum evolution of a charged particle subjected to a uniform
magnetic field and an electric field E(t) that exists for a finite period of
time. The electric field can induce intra-Landau level transitions (magnetic
translations) that do not change the energy of the particle. It may also induce
energy changing inter-Landau level transitions. Our purpose in this paper is
two-fold: We first demonstrate that the inter-Landau level transition
probability is completely determined by the Fourier component of the electric
field corresponding to the cyclotron frequency. Then we point out that the
Fejer asymptotic form of Laguerre polynomials implies that no matter how small
the Fourier component is inter-Landau level transition probability from a fixed
Landau level to other energy levels can be arbitrarily close to 1 if the
original Landau energy level is high enough, i.e., influenced by a given
electric field, Landau levels of higher energy are less stable asymptotically
and their transition probabilities are explicitly predicted by the Fejer
formula.
