The influence of moving boundaries on the stability of quantum Hamiltonian
systems, in particular on the dynamics of quantum versions of the classical
Pustilnikov model, is investigated (the latter consists of a masspoint bou
ncing above an oscillating plate under the influence of constant gravity.)
It is shown that, in contrast to the classical Pustilnikov model, generic t
ime-periodic boundary conditions (including the Dirichlet condition) on the
quantum models do not allow unlimited energy gain ("speeding up") of these
systems.