Question: For the examples in Problem 11.24 (c) and (d), calculate C m (t), to first order. Check the normalization condition: and comment on any discrepancy.

For the examples in Problem 11.24 (c) and (d), calculate C_m(t), to first order. Check the normalization condition:

012 = 1, m (11.122)

and comment on any discrepancy. Suppose you wanted to calculate the probability of remaining in the original state Ψ_N; would you do better to use

Problem 11.24 (c) and (d)

(c) For example, suppose Ĥ' is constant (except that it was turned on at t = 0, and switched off again at some later time . Find the probability of transition from state N to state M (M ≠ N), as a function of T.

(d) Now suppose Ĥ' is a sinusoidal function of time: Ĥ' = VCos(ωt). Making the usual assumptions, show that transitions occur only to states with energy EM = EN ± ћω, and the transition probability is

012 = 1, m (11.122)

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