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Please answer the question below in a clean and correct manner as quick as you can

. Questions are associated to Introductory Quantum Mechanics.

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6.png

6.png
Problem 6.
Consider electron in a spin state
126) = cos(@/2) |= = ) + sin(a/2) |2 -2 ) ,
(10)
where o is a parameter, and
NIF
are the common eigenstates of the total spin
square operator S' and the spin operator in a-direction S, with quantum numbers
s = 1/2, m. = 11/2, respectively.
Now put this state in an external magnetic field pointing along a direction in the
r-y plane,
B = Bri+ By + +Be ,
(11)
where r, y, & are unit vectors pointing along the r, y, z-axis, respectively. The inter-
acting Hamiltonian of the electron spin with the magnetic field takes the form
Hint = -S . B ,
me
(12)
where m. is the electron mass.
Use the matrix representation of spin states and operators to derive the average
of the Him operator under the above spin state ().

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