Consider a particle of mass m in a one-dimensional infinite square well with V(x) = 0 for 0 ≤ x ≤ a and V(x) = elsewhere. A time-dependent perturbation is added of the form 2x V₁(x,t) = = ε - 1 sin(wt) for 0 ≤ x ≤ a a = ∞ If initially the particle is in the ground state, calculate the probability that it will make a transition to the first excited state.

Consider a particle of mass m in a one-dimensional infinite square well with V(x) = 0 for 0 ≤ x ≤ a and V(x) = elsewhere. A time-dependent perturbation is added of the form 2x V₁(x,t) = = ε - 1 sin(wt) for 0 ≤ x ≤ a a = ∞ If initially the particle is in the ground state, calculate the probability that it will make a transition to the first excited state.