(a) Use Eqn. (2.41) or (2.40) to find the eigenvectors and eigenvalues of a spinmeasurement aligned at a 45 degree from both the x- and z- axes (in the x-Zplane; no y component).(b) Suppose you carry out this measurement on a spin-up state (|+)). What out-comes might you find, and which which probabilities for each?(c) Suppose the actual outcome is the least likely possibility, in one particularinstance. After this measurement, you measure S2. Now what might you find,and which which probabilities for each? The spin component along this direction is obtained by projecting the spin vector S onto this new unitvectorS, = S•în(2.40)S, sin 0 cos o + S, sin 0 sin + S¸ cos 0.%3DThe matrix representations we found for S,, S,, and S, lead to the matrix representation of the spincomponent operator S„ (Problem 2.6):sin e e-iøh ( cos0S.2 \sin0 e' -cos0(2.41)

Answered: Image /qna-images/answer/8eb0f651-5f39-4a41-ab57-5265b990d40f.jpg

Answered: (a) Use Eqn. (2.41) or (2.40) to find…

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