QM: spin

  • Thread starter rsaad
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  • #1
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Homework Statement



Find the eigenvalues and eigenstates of the spin operator S of an electron in the direction
of a unit vector n; assume that n lies in the xz plane.

Homework Equations



S|m>= h m|m>


The Attempt at a Solution



This question is from Zettili QM and they have written:

n.S|m>= (h/2) m|m>

I do not understand why are they taking a half.
If I take m=1/2 in S|m>= (h/2) m|m>, I get h/4 but the answer should be h/2, by using S|m>= h m|m>.
So where am i going wrong?
 

Answers and Replies

  • #2
BruceW
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m is the quantum number. you need to check its definition
 
  • #3
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Of course it is a quantum number but why is there a half?
 
  • #4
vela
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It's probably just a typo. It doesn't really matter, though. It just means the quantum numbers are ##\pm1## instead of ##\pm 1/2##.
 
  • #5
BruceW
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I see now. The notation in the two equations is not consistent.
S|m>= h m|m>
n.S|m>= (h/2) m|m>
In the second equation, m is a 'quantum number' (i.e. integer), while in the first equation I guess you could interpret m as the value of the projection of angular momentum, in natural units.
 

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