Quantum Mechanics expectation value problem

[rockstar101]

Homework Statement

An electron is in the spin state in the Sz representation

|ψ> = A (1-2i 2)T <- this is a 2 X 1 matrix

If Sx is measured, what values and probabilities do you get?
What is the expectation value of Sx?

Homework Equations

The Attempt at a Solution

So first, I need to find what A equals to:

A^2 [ (1-2i)(1+2i)+ 4 ] = 1
thus A = 1/3

now, I need to know what values of Sx I would get and the probabilities to
proceed to find the expectation value.

What values of Sx would I get? could it be just +/- h-bar/2 ??
What would be the probabilities??

I would really appreciate any hint or help!

 

[gabbagabbahey]

Homework Statement

An electron is in the spin state in the Sz representation

|ψ> = A (1-2i 2)T <- this is a 2 X 1 matrix

I assume you mean

$$|\psi\rangle=A\begin{pmatrix}1-2i&2\end{pmatrix}^T=A\begin{pmatrix}1-2i\\2\end{pmatrix}$$

?

now, I need to know what values of Sx I would get and the probabilities to
proceed to find the expectation value.

What values of Sx would I get? could it be just +/- h-bar/2 ??
What would be the probabilities??

I would really appreciate any hint or help!

What is the matrix representation of $S_x$ in the z-basis? What are its eigenvalues and eigenvectors?