Effects of quantum geometric phase of a particle in an oscillating hard-wall spherical trap

We obtained the geometric phase for states of a particle in a spherical infinite potential well with moving walls in two different cases: First, when the radius of the well increases (or decreases) monotonically. Secondly, when the radius changes are oscillatory. In the latter case, we have solved the Schrödinger equation and found its solutions approximately. We obtained the transition rate for the possible real situation in an acousto-optic case which can reveal the effect of the geometric phase. We show that the absorption or radiation peaks will appear if the energy gap between the incident photon and the modified energy difference of two levels by the geometric phase is equal to the integer multiple of oscillation frequency.