- 18

- 0

_{x}]

[tex]\chi = \frac{a+b}{\sqrt{2}}\chi^{(x)}_+ + \frac{a-b}{\sqrt{2}}\chi^{(x)}_-[/tex]

What I don't understand (among other things) is why S

_{y}and S

_{z}don't count. Because there are only to directions, up and down? (If so, how do I know which of S

_{x},S

_{y}and S

_{z}to choose?)

Another thing is that I'm told that a spin in the direction (x,y,z) is defined as [tex]\textbf{S}=\frac{\hbar}{2}(x\sigma _x +y\sigma _y +z\sigma _z)[/tex]. What exactly is this and how does it relate to the spinor? It is a matrix but a spinor (that's also supposed to describe the spin state) is a vector.