  We calculate transition amplitudes and probabilities between the coherent and
Fock states of a quantum harmonic oscillator with a moving center for an
arbitrary law of motion. These quantities are determined by the Fourier
transform of the moving center acceleration. In the case of a constant
acceleration, the probabilities oscillate with the oscillator frequency, so
that no excitation occurs after every period. Examples of oscillating and
rotating motion of the harmonic trap center are considered too. Estimations
show that the effect of excitation of vibration states due to the motion of the
harmonic trap center can be observed in available atomic traps.
