We can determine f(t) by first studying its Fourier transform, \[F(\omega) \;=\; \int_{-\infty}^\infty dt \; e^{i\omega t}\, f(t) \;=\; \int_0^\infty dt \; e^{i(\omega + i\varepsilon) t} \; \langl...We can determine f(t) by first studying its Fourier transform, F(ω)=∫∞−∞dteiωtf(t)=∫∞0dtei(ω+iε)t⟨φ|e−iˆHt/ℏ|φ⟩. Now insert a resolution of the identity, ˆI=∑n|n⟩⟨n|, where {|n⟩} denotes the exact eigenstates of ˆH (for free states, the sum goes to an integral in the usual way): \[\begin{align} \begin{aligned}F(\…
