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The Pauli Spin matrices, 01 $₁=1 (16). $. = 1 (15) Ŝx Sy 0 and S₂ = = 4 (6-91) a) Using direct matrix multiplication to find their commutation relations. They should be exactly the same as the angular momentum. b) Calculate the matrix for $2. This is a special matrix, but the factor you get in front of this matrix is A or 1(1+1) from the angular momentum case.

The Pauli Spin matrices, 01 $₁=1 (16). $. = 1 (15) Ŝx Sy 0 and S₂ = = 4 (6-91) a) Using direct matrix multiplication to find their commutation relations. They should be exactly the same as the angular momentum. b) Calculate the matrix for $2. This is a special matrix, but the factor you get in front of this matrix is A or 1(1+1) from the angular momentum case.

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The Pauli Spin matrices, 5.-1(b) Sv=1 (1) and 5₁=1 (0-1) (ió). x = i a) Using direct matrix multiplication to find their commutation relations. They should be exactly the same as the angular momentum. b) Calculate the matrix for $2. This is a special matrix, but the factor you get in front of this matrix is A or 1(1+1) from the angular momentum case. c) Let's say we have some eigenstate of the operator $² and $₂,4 = |s, 8₂ >. Using the factor you found from part b and what we learn about, Ĺ², Îz, & = [1, m >. Deduce the eigenvalues of $² and $₂ on its eigenstates & = |s, s₂ >? Hint: If you use the quadratic formula, one solution would physically make sense while the other does not.
Transcribed Image Text:The Pauli Spin matrices, 5.-1(b) Sv=1 (1) and 5₁=1 (0-1) (ió). x = i a) Using direct matrix multiplication to find their commutation relations. They should be exactly the same as the angular momentum. b) Calculate the matrix for $2. This is a special matrix, but the factor you get in front of this matrix is A or 1(1+1) from the angular momentum case. c) Let's say we have some eigenstate of the operator $² and $₂,4 = |s, 8₂ >. Using the factor you found from part b and what we learn about, Ĺ², Îz, & = [1, m >. Deduce the eigenvalues of $² and $₂ on its eigenstates & = |s, s₂ >? Hint: If you use the quadratic formula, one solution would physically make sense while the other does not.
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