Consider a perturbation to a two-level system with matrix elements where and are positive constants
Question:
Consider a perturbation to a two-level system with matrix elements
where τ and α are positive constants with the appropriate units.
(a) According to first-order perturbation theory, if the system starts off in the state Ca = 1, Cb = 0 at t = -∞, what is the probability that it will be found in the state b at t = ∞?
(b) In the limit that τ → 0, Hab = aδ(t). Compute the τ → 0 limit of your expression from part (a) and compare the result of Problem 11.4.
(c) Now consider the opposite extreme: ω0τ >> 1. What is the limit of your expression from part (a)? Comment: This is an example of the adiabatic theorem (Section 11.5.2).
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Step by Step Answer:
a Using Equation 1121 The probability of a transition then is b In the limit 0 ...View the full answer
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Related Book For 
Introduction To Quantum Mechanics
ISBN: 9781107189638
3rd Edition
Authors: David J. Griffiths, Darrell F. Schroeter
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