Discuss the below:
Tensor Products of Su(2) Operators
Q: In the Hilbert space C^2 x C^2
(where x is used in all of my notation to mean the cross product)
Consider the state vector:
Psi = 1/sqrt(2) ( e_1 X e_2) + 1/sqrt(2) ( e_2 X e_1 )
(Section a)
What is the probability that the measurement of q_3 X I gives the value -1 and how does the state vector change in this case?
(NOTE: where q_3 is sigm_3, X is tensor product, I is identity matrix, and we are in C^2 X C^2)
(Section b)
The same question for the measurement of I x q_3 and the value +1
(Section c)
Find the state vector psi(t) at time t if the Hamiltonian is: q_3 x I + I x q_2