Question

The z-component of the spin of an electron in free space is measured and found to be h/2. (a) If a subsequent measurement is made of the x-component of the spin, what are the possible results? (b) What are the probabilities of finding each of these results? (c) The spin operator along a different axis n defined by the spherical polar angles Î¸ and Ï† with respect to the original coordinate system is given by Sn = nÂ·S. Show that the possible results for the measurement of the spin orientation in this direction are the same as in (a). (d) In this case, the eigenvectors of Sn can be written as cos(Î¸/2) and sin(Î¸/2) e^(iÏ†) cos(Î¸/2) in the basis which diagonalizes Sz. What are the probabilities of the various possible results now? (e) What is the expectation value of a measurement of S for the electron in the h eigenstate of S?

Name: the z component of the spin of an electron in free space is measured and found to beh2 a if a subsequent measurement is made of the x component of the spin what are the possible results b wh 95493
Uploaded: 2023-07-25T13:15:55-08:00
Duration: 21 s
Channel: Numerade
Description: the z component of the spin of an electron in free space is measured and found to beh2 a if a subsequent measurement is made of the x component of the spin what are the possible results b wh 95493

          The z-component of the spin of an electron in free space is measured and found to be h/2.
(a) If a subsequent measurement is made of the x-component of the spin, what are the possible results?
(b) What are the probabilities of finding each of these results?
(c) The spin operator along a different axis n defined by the spherical polar angles Î¸ and Ï† with respect to the original coordinate system is given by Sn = nÂ·S. Show that the possible results for the measurement of the spin orientation in this direction are the same as in (a).
(d) In this case, the eigenvectors of Sn can be written as
cos(Î¸/2) and
sin(Î¸/2) e^(iÏ†) cos(Î¸/2)
in the basis which diagonalizes Sz. What are the probabilities of the various possible results now?
(e) What is the expectation value of a measurement of S for the electron in the h eigenstate of S?

the z component of the spin of an electron in free space is measured and found to beh2 a if a subsequent measurement is made of the x component of the spin what are the possible results b wh 95493

Added by Stephanie H.

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