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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Please help with EXERCISE 5.35
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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