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Exercise 5.35 Consider a particle of spin 32. Find the matrix for the component of the spin along a unit vector with arbitrary direction ǹ. Find its eigenvalues and eigenvectors. Hint: n = (sin cos q)i + (sin sin o)j + (cos 0) k.

Exercise 5.35 Consider a particle of spin 32. Find the matrix for the component of the spin along a unit vector with arbitrary direction ǹ. Find its eigenvalues and eigenvectors. Hint: n = (sin cos q)i + (sin sin o)j + (cos 0) k.

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Exercise 5.34 (a) Find the eigenvalues (call them 21, 22) and eigenstates (21), | 22)) of the spin operator S of an electron when S is pointing along an arbitrary unit vector ʼn that lies within the yz plane. (b) Assuming that the initial state of the electron is given by √√3 =12141)+1/3 122), | y/o) = find the probability of obtaining a value of Ŝ = ħ/2 after measuring the spin of the electron. Exercise 5.35 Consider a particle of spin 32. Find the matrix for the component of the spin along a unit vector with arbitrary direction ǹ. Find its eigenvalues and eigenvectors. Hint: n = (sin cos q)i + (sin sin o)j + (cos)k.
Transcribed Image Text:Exercise 5.34 (a) Find the eigenvalues (call them 21, 22) and eigenstates (21), | 22)) of the spin operator S of an electron when S is pointing along an arbitrary unit vector ʼn that lies within the yz plane. (b) Assuming that the initial state of the electron is given by √√3 =12141)+1/3 122), | y/o) = find the probability of obtaining a value of Ŝ = ħ/2 after measuring the spin of the electron. Exercise 5.35 Consider a particle of spin 32. Find the matrix for the component of the spin along a unit vector with arbitrary direction ǹ. Find its eigenvalues and eigenvectors. Hint: n = (sin cos q)i + (sin sin o)j + (cos)k.
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