Please answer and show me all questions below. I would really appreciate it if you can solve them as soon as possible!!A constant magnetic field B is applied along the +x direction to an electron whose spinor is initially ([1],[0]) in
the S_(z) eigenbasis.
a) What is the matrix representation of Hamiltonian H in the S_(z) eigenbasis? (1 pt)
b) What is the spinor after some time t in the same basis? (3 pts)
c) At time t, what is the probability of finding the spin points towards -Z direction? (1 pt)
d) At time t, what is the expectation value of the spin angular momentum along the y axis, (:S_(y):) ? (2 pts)
e) At time t, the first spin measurement is performed along the z axis and the spin is found to point towards the
-z direction. What might one find if the second spin measurement along the z axis is immediately followed?
Please also comment on the possible measurement results and their corresponding probabilities if the second
immediate spin measurement is instead performed along the y axis. ( 3 pts)
5. A constant magnetic field B is applied along the +x direction to an electron whose spinor is initially (
the Sz eigenbasis.
a) What is the matrix representation of Hamiltonian H in the Sz eigenbasis? (1 pt)
b) What is the spinor after some time t in the same basis? (3 pts)
c) At time t, what is the probability of finding the spin points towards --z direction? (1 pt)
d) At time t, what is the expectation value of the spin angular momentum along the y axis, (Sy) ? (2 pts)
e) At time t, the first spin measurement is performed along the z axis and the spin is found to point towards the -z direction. What might one find if the second spin measurement along the z axis is immediately followed? Please also comment on the possible measurement results and their corresponding probabilities if the second immediate spin measurement is instead performed along the y axis. (3 pts)