time dependent perturbation theory

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at t=0,

Turn on perturbation and at a later time, what is the probability of a transition from ?

with then p(transition) = .

Use time dependent schrodinger equation to get:

. Projecting out, you get: . .

The time dependent perturbation expansion gives:

. Do a series expansion. This gives:

• 0th order:
• 1st order:
• 2nd order:
• Exactly: is the exact dyson sum.

Example:

• oscillating magnetic field

source psfile jl@crush.caltech.edu index oscillating_magnetic_field perturbation_theory