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Nice one, just a clarification(in your second last para about discrete spectrum). As I change t0
little bit, to sayt1=t0+δ, we get new quasi energy, because we know U(t0+T,t0) gives ϵ0(which is precisely the phase quantum state has acquired during that evolution) and similarly U(t1+T,t1) will give ϵ1
? – L.K. 1 hour ago deleted by dmckee♦ 12 mins ago undelete
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@L.K. No, the quasi-energy doesn't change. The propagator formulation is a fancy restatement of |Ψ(t)⟩=e−iεt|Φ(t)⟩
, where |Φ(t)⟩ is periodic; on that subspace, the propagator reads U(t,t′)=|Ψ(t)⟩⟨Ψ(t)|=e−iε(t−t′)|Φ(t)⟩⟨Φ(t)|. …