Wavefunction, energy spectrum and uncertainty relation for a particle contained between moving potential walls

The temporal energy spectrum Esup(s,a)(t) and the uncertainty product δpsup(s,a)(t)δxsup(s,a)(t) are derived from an analytical solution psi(x,t) of the initial-boundary-value problem for the Schroedinger equation of a particle contained between moving potential walls at x = +-s(t), which are set in motion according to an arbitrary (non-relativistic) translation s = s(t) at time t = O. Both symmetrical (s) and antisymmetrical (a) particle states are considered as initial conditions in the region -s(O) <= x <= + s(O). The physical implications of the compression and expansion of the probability density by the moving walls on the wave mechanics of the particle are discussed. The results are understandable within the statistical interpretation of quantum theory. (author)