We investigate the effect of time-dependent boundary conditions on the
    dynamics of a quantum bouncer — a particle falling in a homogeneous
    gravitational field on a moving mirror. We examine more particularly the way a
    moving mirror modifies the properties of the entire wavefunction of a falling
    particle. We find that some effects, such as the fact that a quantum particle
    hitting a moving mirror may bounce significantly higher than when the mirror is
    fixed, are in line with classical intuition. Other effects, such as the change
    in relative phases or in the current density in spatial regions arbitrarily far
    from the mirror are specifically quantum. We further discuss how the effects
    produced by a moving mirror could be observed in link with current experiments,
    in particular with cold neutrons.

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