Average energy and Shannon entropy of a confined harmonic oscillator in a time-dependent moving boundary

The time-dependent Schrödinger equation for a particle in a radically confined quantum harmonic oscillator is considered analytically under the influence of a moving boundary condition. Two distinct special cases corresponding to (a) uniformly varying radius and (b) parabolic radius are discussed. These offer solutions in terms of confluent hyper-geometric functions. Beside, the periodic special case is also considered, in which case, the solutions are obtained in terms of Bessel functions. Quantities such as expectation values as well as time-dependent radial density distribution function, time-dependent average energy are obtained in terms of radius of the spherical impenetrable box, in each case. These are considered here for the first time. In addition the Shannon entropy of the radial density functions are calculated quasi exactly.