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σy<br />
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<br />
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n αβ<br />
r<br />
n Tr<br />
r<br />
δ αβ<br />
m r<br />
<br />
σ αβ<br />
2<br />
m r<br />
¤∑<br />
n αβ<br />
αβ<br />
r<br />
<br />
σ αβ<br />
n Tr<br />
r Tr<br />
n αβ<br />
r<br />
α<br />
¤∑<br />
n αα<br />
r<br />
Pauli sp<strong>in</strong> matrices,<br />
σ¤<br />
σx<br />
σ z<br />
0 1<br />
0<br />
i<br />
1 0<br />
σ x¤<br />
1 0<br />
σy¤<br />
i 0<br />
σz¤<br />
0<br />
1<br />
M. MARSMAN, <strong>VASP</strong> WORKSHOP, VIENNA 10-15 FEBRUARY 2003. Page 4
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