Question

I. The state vector φ(t) at time t can be decomposed on the {I +), l-)} basis: Write down the system of coupled differential equations which the components c+ (t) and c() satisfy 2. Let |φ(1-0)) be decomposed on the {lx+), lx-) basis. Show that c+(1)-(Ηφ(t)) is written as sin with Ω 2VA2+B2. Here f.Ω is the energy difference of the two levels. Show that c+(1) (as well as c (t)) satisfies the differential equation c) 0. We assume that c+ (0) of finding the system in the state |+) at time t is 3. Find λ and μ up to a phase as well as c+(t). Show that the probability p+(r) = sin'θ sin' ( )--82 Sin 4. Show that if c+(1-0) = 1, then c+ (t) = cos i cos θ sin-. Find p, () and p_(1), and verify that the result is compatible with that of the preceding question.

Answer 1

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