Consider a rotation of a spin s = 1/2 atom around the y axis by an angle 0. (i) Write down the rotation operator, and (ii) determine the state of the atom after the rotation if it was initially in the eigenstate of the operator S. corresponding to the eigenvalue +h/2. (iii) Calculate all the possible values of the angle 0 that are consistent with the probability p- = 3/4 of obtaining the eigenvalue -h/2 when the measurement of the z-component of spin angular momentum S, is performed on the rotated state.
Consider a rotation of a spin s = 1/2 atom around the y axis by an angle 0. (i) Write down the rotation operator, and (ii) determine the state of the atom after the rotation if it was initially in the eigenstate of the operator S. corresponding to the eigenvalue +h/2. (iii) Calculate all the possible values of the angle 0 that are consistent with the probability p- = 3/4 of obtaining the eigenvalue -h/2 when the measurement of the z-component of spin angular momentum S, is performed on the rotated state.
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Transcribed Image Text:Consider a rotation of a spin s = 1/2 atom around the y axis by an angle 0.
(i) Write down the rotation operator, and
(ii) determine the state of the atom after the rotation if it was initially in the eigenstate
of the operator S, corresponding to the eigenvalue +h/2.
(iii) Calculate all the possible values of the angle 6 that are consistent with the probability
p- = 3/4 of obtaining the eigenvalue -h/2 when the measurement of the z-component of
spin angular momentum Š, is performed on the rotated state.
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