zheng89120
Mar26-11, 01:05 AM
1. The problem statement, all variables and given/known data
Consider a three level system, the time-dependent perturbation is:
W(t) = W cos(wt) e^(-t^2/T^2)
at time t=-infinity, it's in the ground state (w/ E1)
the pertubation frequency is:
w = (w21+w31)/2
non-zero matrix elements are: <1|W|2>=<1|W|3>=<2|W|1>=<3|W|1>=\gamma
Show that the eigenstate is:
|\psi(t)> = e-iw1t [ ||\psi>
-iAe-iw21t |\psi>
-iAe-iw31t |\psi3> ]
2. Relevant equations
fourier transform of a gaussian
3. The attempt at a solution
tried to take fourier transform of cos wt * e^(-t^2/T^2), but couldn't get the form Aeiwt |\psi2/3>
Consider a three level system, the time-dependent perturbation is:
W(t) = W cos(wt) e^(-t^2/T^2)
at time t=-infinity, it's in the ground state (w/ E1)
the pertubation frequency is:
w = (w21+w31)/2
non-zero matrix elements are: <1|W|2>=<1|W|3>=<2|W|1>=<3|W|1>=\gamma
Show that the eigenstate is:
|\psi(t)> = e-iw1t [ ||\psi>
-iAe-iw21t |\psi>
-iAe-iw31t |\psi3> ]
2. Relevant equations
fourier transform of a gaussian
3. The attempt at a solution
tried to take fourier transform of cos wt * e^(-t^2/T^2), but couldn't get the form Aeiwt |\psi2/3>