••• (Section 11.5) Consider the electron of Problem 1, which is initially in the n = 2 state Ψ2 of the infinite square well with width a = 1. When an electric field ℰ is switched on for a brief time Δt, the wave function picks up a small component proportional to xΨ2(x). (a) Use a suitable plotting program to make plots ofΨ2(x) and Ψ2(x). (b) It is probably not immediately clear what the extra wave function xΨ2(x) (multiplied by a small constant) signifies. To clarify this, expand xΨ2(x) as in (11.20), and find the coefficients Am of this expansion. Use your answer to argue that, to a good approximation, the extra wave function has the form xΨ2(x) ≈ A1Ψ1(x) + A3Ψ3(x). Plot the right-hand side of this approximation, and compare with your plot of xΨ2(x). What is the physical significance of this result?
Problem 1
•• Consider an electron that is initially in the first excited state of the infinite square well of Example 11.4 (Sec. 11.5). (a) If an electric field ℰ is switched on in the x direction, find the probability P(2 → 1 ) that the electron will be found in the ground state a short time Δt later, (b) Similarly, find the probability P(2 → 3) for excitation to the second excited state, (c) What are P(2 → 4) and P(2 → 5)? Compare these various probabilities.
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