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Expectation values for spin

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The spin state is:

ksi = A [1-2i, 2]

In general the norm of a state [a, b] is |a|^2 + |b|^2. If we take A to be real, then:

|ksi|^2 = A^2 (|1-2i|^2 + |2|^2) = A^2 (5+4) = 9 A^2.

ksi is correctly normalized if

|ksi|^2=1 ---->

9 A^2 = 1 ---->

A = 1/3

Now, for a generic spin 1/2 state you can find the values hbar/2 and -hbar/2 if you measure the spin in some direction. The exception is when the spin is in an eigenstate of the spin operator for that direction, in which case you can only find the eigenvalue corresponding to that eigenstate, which can be either hbar/2 or -hbar/2. But in such a case, the expectation ...

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