Finding Probabilities for Electron Spin in Quantum Mechanics

[foranlogan2]

The spin of an electron is described by a vector psi = column vector with two entries,psi up and psi down

Give the general expressions for the probabilities to find Sz= +or- h/2 in a measurement of S^z

where Sz=h/2(1 0) as a matrix
( 0 -1)


ii)Give the general expressions for the probabilities to find <S^z>

culd anyone help,i can't find the general expressions for the probabilitites in my notes.

 

[Meir Achuz]

Expand the given column vector in terms of pure up (1,0) and pure down (0,1)
as u=a u(up) + b u(down).
Then the proballiites are4 |a|^2 and |b|^2.