PHYSICS 137B Study Guide - Midterm Guide: Geometric Phase, Rabi Frequency, Ladder Operator
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Hints: several problems may be solved without calculation, or very little calculation. The amplitudes for the two states are ca(t), cb(t). ca(t) = [cos( t cb(t) = i. 2 ) + i sin( t sin( t. 2 ) ei t/2, (1) (2) where = 2 and = 0 is the detuning. R + 2, r = vab/ is the rabi frequency: 10 points what are the initial conditions ca(0), cb(0) of this solution, 10 points find the solution for initial conditions ca(0) = 0, cb(0) = 1. Hint: you don"t need to solve the di erential equations for the two-level system from scratch. Instead, modify the above solution: 10 points assume = 0. The system is initially in the ground state |0 . In each case, calculate the probability of nding the system in the state |1 at a time t after the perturbation has initially been switched on.
