Principles of Quantum Mechanics · Problem 18.10

Time-Dependent Perturbation Theory — R. Shankar

Physics — Quantum Mechanics · sudden-approximation

Problem

The ground state of hydrogen is perturbed by a (time-independent) uniform electric field E=E0z^\mathbf{E} = E_0 \hat{z}, but now the perturbation is suddenly turned off at time TT. Using the results of Chapter 7 for time-independent perturbation theory: (a) What is the wave function at t=0+t = 0^+ (just after the field is turned on)? (b) What is the wave function at time T−T^- (just before the field is turned off)? (c) What is the wave function at time T+T^+ (just after the field is turned off)? (d) What is the probability that the atom is found in state ∣2,1,0⟩|2, 1, 0\rangle at time T+T^+?

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