How Do You Normalize Quantum States and Calculate Spin Expectation Values?

[foranlogan2]

The spin of an electron is described by a vector
spinor and the spin operator
^S = ^ Sxi + ^ Syj + ^ Szk with components


how would i go about normalizing a state like the one below,i am miles away to what is going on here

c) (i) Normalise the state (1 1) *this is meant to be a column vector*

ii) calculate expectation values for <Sx> ,<Sy> and <Sz>


Sx = h/2(0 1) Sy = h/2(0 -i ) Sz = h/2(1 0)
(1 0) ( i 0 ) (0 -1)

any help on this would be greatly appreciated.because being honest i am lost
thanks

 

[Meir Achuz]

You need a better text or some tutoring.
You need more help than you can get here.
Normalize means just make u^{dagger}u=1.
Exp. value=u^{dagger}[s_x[u, using matrlix multiplication,
with [s_x] a 2X2 matrix.