Quantum bouncer on a spring

The usual 'quantum bouncer' is a quantum particle bouncing elastically under the influence of gravity. Here we consider a particle bouncing off an impenetrable wall, and bound to it by the harmonic potential 1/2 m omega(2)x(2) instead of by the gravitational potential mgx. An analytic solution is possible, easily accessible to classes in intermediate quantum mechanics. The solution is related to Schrodinger's oscillating wavepacket (the original coherent state). Although periodic, it changes its form during the oscillation, in contrast to Schrodinger's packet. The uncertainties in the position (Delta x) and the momentum (Delta p) oscillate also, as does the product Delta x Delta p.