Derive and expression for the probability that an incident

Question

Consider a particle with charge q and mass m in the ground state of the spherically symmetric potential

V(r) = 1/2mω²(r² -r₀²) for r < r_o and V(r) = 0 for r > r₀.

Derive and expression for the probability that an incident electromagnetic wave A^→(r^→ t) = A_o^→cos(k^→.r^→ - ωt) pops the particle out of the potential well.

Approximate the ground state as the harmonic oscillator ground state and then make the same assumptions and approximations as when we discussed the ionization of the hydrogen atom by an incident electromagnetic wave in class.