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For a spin 1 system l = 1 and m = -1 , 0 , 1. For the operator <math>S_{z}</math> we have | For a spin 1 system l = 1 and m = -1 , 0 , 1. For the operator <math>S_{z}</math> we have | ||
<math>S_z |l,m \rangle</math> \Rightarrow <math> \langle l,n| S_z|l,m \rangle = m\hbar \langle l,n|l,m \rangle</math> <math>\Rightarrow ( S_z)_{nm} = m\hbar \delta _{nm}</math> | <math>S_z |l,m \rangle</math> <math>\Rightarrow</math> <math> \langle l,n| S_z|l,m \rangle = m\hbar \langle l,n|l,m \rangle</math> <math>\Rightarrow ( S_z)_{nm} = m\hbar \delta _{nm}</math> | ||
So | So | ||
| Line 13: | Line 12: | ||
0 & 0 & -1 \\ | 0 & 0 & -1 \\ | ||
\end{pmatrix}</math> \Rightarrow | \end{pmatrix}</math> <math>\Rightarrow</math> | ||
<math> S_{z}^{2} = {\hbar}^2\begin{pmatrix} | <math> S_{z}^{2} = {\hbar}^2\begin{pmatrix} | ||
1 & 0 & 0 \\ | 1 & 0 & 0 \\ | ||
Revision as of 23:05, 30 April 2010
For a spin 1 system l = 1 and m = -1 , 0 , 1. For the operator we have
So
