Question: Consider a two-level system with E 1 2. There is a time-dependent potential that connects the two levels as follows: At t = 0, it

Consider a two-level system with E₁ 2. There is a time-dependent potential that connects the two levels as follows:

At t = 0, it is known that only the lower level is populated-that is, c₁(0) = 1, c₂(0) = 0.

(a) Find

by exactly solving the coupled differential equation

(b) Do the same problem using time-dependent perturbation theory to lowest nonvanishing order. Compare the two approaches for small values of λ. Treat the following two cases separately:

(i) ω very different from ω₂₁ and

(ii) ω close to ω₂₁·

V11 = V22=0, V12=yeiwl, V1=ye-iar (y real).

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