1. Determine the action of the spin raising and lowering operators on the eigenstates of I2 and L, Is, m,), and determine the matrix form of these operators in the spin 1/2 basis. 2. Determine the matrix form of the operators S and S, in the spin 1/2 basis 3. Determine the commutation relations between the Pauli matrices for the spin 1/2 basis. 4. Determine the eigenstates and eigenvalues of the S, operator 5. Let the spinors (0)=and (1)=( form the spin 1/2 basis.Let the Hadamard operator be such that H(0) = (+) and Ha|1) = |), where {+),)} form the eigenstate basis of the S operator. Determine the matrix form of the Hadamard operator. 6. Given a general state
cos(/2)eBt/2 = (sin (/2)e-iB1/2
Determine
a) The expected value of the S, operator
b) The expected value of the S operator
c) The expected value of the S operator
Let (00) = , [I ) - | )] be the singlet state formed by the combination of two spin-1/2 particles. Determine
a) S(00)
b) S_|O0}
c) S2(00}
Repeat the operations from question 7 for the three triplet states.
