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Consider an electron at rest in the magnetic field:
B = B0x^,
where B0 is constant.
(a) Show that the Hamiltonian matrix in the Sz representation is
b) What are the eigenvalues for energy, and the corresponding eigenvectors?
(c) Assume the electron is in the spin-down state along the z axis at time t = 0:
|ψ(t=0)> = |->.
Determine the quantum state |ψ(t)> of the electron at a later time t. Express your result in terms of the basis for measurement of Sz.
(d) What is the expected value of the energy at time t?
(e) Determine the probability of a spin flip in z, i.e. calculate
P+ = |<+|ψ(t)>|2
and sketch your result as a function of t.
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