Two classes of exactly solvable quantum models with moving boundaries

It is shown here that the non-stationary Schrodinger equation can be solved exactly for two quantum models subject to Dirichlet boundary conditions. One of them is a modified problem of a quantum bouncer, i.e. the problem of a particle falling down in the gravitational field on a moving (oscillating) platform such as a loudspeaker. The second model is a 'cuff-off oscillator' with a moving infinite potential wall and a time-dependent frequency. In both cases exact solutions are given in closed forms, easy to use. Their possible applications are also indicated. In each of the models extra coordinate- and time-dependent phase factors are generated by moving boundaries in the former case giving rise to a non-local effect in quantum mechanics.

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