A particle of spin ; is described by a wave function for which the dependence on the angular coordinates 0, o and on the spin o is given by 21 – 1 2 V(0, 6; 0) = Yı1-1(0, ¢) |H) – Yı-2(0, ¢) |T) - 21 +1 21 +1 Here l>2 is an integer, and Yım(0, 0) are spherical harmonics, which are eigenstates of the orbital angular momentum operators L2 and L.. It) = X1/2,1/2 and 4)=X1/2,-1/2 are normalized eigenstates (spinors) of the spin operators S² and Sz with S²-eigenvalue h? and with S-eigenvalues +h and -h, respectively.
A particle of spin ; is described by a wave function for which the dependence on the angular coordinates 0, o and on the spin o is given by 21 – 1 2 V(0, 6; 0) = Yı1-1(0, ¢) |H) – Yı-2(0, ¢) |T) - 21 +1 21 +1 Here l>2 is an integer, and Yım(0, 0) are spherical harmonics, which are eigenstates of the orbital angular momentum operators L2 and L.. It) = X1/2,1/2 and 4)=X1/2,-1/2 are normalized eigenstates (spinors) of the spin operators S² and Sz with S²-eigenvalue h? and with S-eigenvalues +h and -h, respectively.
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Transcribed Image Text:A particle of spin ; is described by a wave function for which the dependence
on the angular coordinates 0, o and on the spin o is given by
21 – 1
2
V(0, 6; 0) =
Yı1-1(0, ¢) |H) –
Yı-2(0, ¢) |T) -
21 +1
21 +1
Here l>2 is an integer, and Yım(0, 0) are spherical harmonics, which are
eigenstates of the orbital angular momentum operators L2 and L..
It) = X1/2,1/2 and 4)=X1/2,-1/2 are normalized eigenstates (spinors) of the
spin operators S² and Sz with S²-eigenvalue h? and with S-eigenvalues
+h and -h, respectively.
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