An electron is at rest in an oscillating magnetic field where B 0 and are constants.

An electron is at rest in an oscillating magnetic field

where B₀ and ω are constants.
(a) Construct the Hamiltonian matrix for this system.
(b) The electron starts out (at t = 0) in the spin-up state with respect to the x axis (that is Determine x(t) at any subsequent time. Beware: This is a time-dependent Hamiltonian, so you cannot get x(t) in the usual way from stationary states. Fortunately, in this case you can solve the time-dependent Schrödinger equation (Equation 4.162) directly.

(c) Find the probability of getting -ћ/2 , if you measure S_x .

(d) What is the minimum field (B₀) required to force a complete flip in S_x?

Equation 4.162

Transcribed Image Text:

B = Bocos (wt) k,