Spin Prob 1: Difference between revisions
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(a) The spin state function <math>\psi_{p}</math> of P is the eigenfunction of <math>\S_{x}</math> with eigenvalue <math>+\frac{\hbar}{2}</math>. So <math>\psi_{p}=\frac{\alpha+\beta}{\ | (a) The spin state function <math>\psi_{p}</math> of P is the eigenfunction of <math>\S_{x}</math> with eigenvalue <math>+\frac{\hbar}{2}</math>. So <math>\psi_{p}=\frac{\alpha+\beta}{\sqrt{2}}</math> | ||
Revision as of 00:41, 29 April 2010
Problem 1:(Added by Hang Chen's group)
P is a beam of atoms with spin quantum number 1/2 and zero orbital angular momentum, all with angular momentum along the x axis. Q is a beam of similar but unpolarised atoms.
(a) What's the spin state function of P in terms of and , the eigenfunctions of ?
(b) If the two beams are passed separately through a Stern-Gerlach apparatus with its magnetic field along the z axis, is there any difference between the emerging beams in the two cases?
(c) How could the difference between P and Q be detected experimentally?
Solution:
(a) The spin state function of P is the eigenfunction of with eigenvalue . So
