Thanks Peter and DrClaude, I think you may have led me to my mistake.
When I looked at S=Sx+Sy+Sz and squared both sides, I dropped the cross terms, ie, SxSy, SxSz, SySz thinking they are orthogonal. But these are 2x2 matrices, so they are not 0. In fact, they are all (hbar/2)^2.
This...
ok, so I think I almost have it, thanks for the help.
S^2=Sx^2+Sy^2+Sz^2
S^2 |z+>= Sx Sx |z+>+SySy|z+>+SzSz|z+>=(hbar/2)^2 * 3 |z+>
S=hbar/2*sqrt(3)
If I got this right, then shouldn't
S=Sx+Sy+Sz ?
And if you go through the same calculation, you get
S=3 hbar/ 2
Thanks for hanging in there...
Thanks again for the response, I appreciate it.
I think you hit the essence of my problem, although I can't give you an anwers.
A spin operator measures the value of a particles spin.
The spin formula by quantum number, S, is:
"The expression √(s(s+1))ħ represents the magnitude of the spin...
Sorry for the lack of clarity.
Let's take S_z |z;+> = hbar/2 |z;+> but I think all spin operators in any direction have the same eigenvalue, hbar/2
And yes, mea culpa, I left off the sqrt. As you said, it's
S = sqrt(s(s+1))hbar I thought this was a common formuler for spin, it's on the...
Assume spin 1/2 particle
So the spin operator gives +/- hbar/2
eg. S |n+> = +/- hbar/2 |n+>
But S= s(s+1) hbar = sqrt(3)/2 hbar
So I'm off by a factor of sqrt(3).
I suspect I am missing something fundamental about my understanding of spin.
My apologies and thanks in advance.
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