An electron is subject to a uniform, time-independent magnetic field of strength B in the positive z-direction.
Question:
An electron is subject to a uniform, time-independent magnetic field of strength B in the positive z-direction. At t = 0 the electron is known to be in an eigenstate of S • n̂ with eigenvalue h̄/2, where n̂ is a unit vector, lying in the xz-plane, that makes an angle β with the z-axis.
(a) Obtain the probability for finding the electron in the sx = h̄ /2 state as a function of time.
(b) Find the expectation value of sx as a function of time.
(c) For your own peace of mind, show that your answers make good sense in the extreme cases
(i) β → 0 and
(ii) β → π/2.
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To solve this problem we need to work with the timeevolution of the state of the electron in the pre...View the full answer
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