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25. 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
V₁(x, t) = Ɛ
(
Xx 1
-
e
for 0 < x <a
a
If initially the particle starts in the ground state, calculate the probability that it will make a transition to the first excited
state. What happen to this result in the limit 7 → ∞?

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