- #1
genloz
- 76
- 1
Homework Statement
Construct the spin matrices ([tex]S_{x}[/tex], [tex]S_{y}[/tex], and [tex]S_{z}[/tex]) for a particle of spin 1. Determine the action of [tex]S_{z}[/tex], [tex]S_{+}[/tex], and [tex]S_{-}[/tex] on each of these
states.
Homework Equations
[tex]S=\sqrt{1(1+1)}\hbar [/tex]
m=-s,-s+1,...,s-1,s
The Attempt at a Solution
m=-1,0,0,0,0,0,0,0,-1
[tex]S=\sqrt{2}\hbar [/tex]
[tex]S_{z}=\hbar \[ \left( \begin{array}{ccc}
1 & 0 & 0 \\
0 & 0 & 0 \\
0 & 0 & -1 \end{array} \right)\] [/tex]
So I understand where [tex]S_{z}[/tex] comes from... I know what the answers for the matrices are from http://en.wikipedia.org/wiki/Pauli_matrices but I don't know how to go about finding [tex]S_{x}[/tex] and [tex]S_{y}[/tex] even with the commutation laws etc... and I don't really understand what it means by 'the action of' in the second part despite numerous searchs on google...
Any help is much appreciated, thankyou!