Finding the Eigenstate of S2 for a Spin 1 Particle

[Jammy453]

Homework Statement

I'm trying to show the Eigenstate of S² is 2ħ^2 given the matrix representations for S_x, S_y and S_z for a spin 1 particle

Homework Equations

S_x = ħ/√2 *
\begin{pmatrix}
0 & 1 & 0 \\
1 & 0 & 1 \\
0 & 1 & 0
\end{pmatrix}

S_y = ħ/√2 *
\begin{pmatrix}
0 & -i & 0 \\
i & 0 & -i \\
0 & i & 0
\end{pmatrix}

S_z = ħ*
\begin{pmatrix}
1 & 0 & 0 \\
0 & 0 & 0 \\
0 & 0 & -1
\end{pmatrix}

(I'm sorry I don't know how to format matrixes on here...)

The Attempt at a Solution

I've tried squaring all the matrices and adding them together but I just get

2ħ² *
\begin{pmatrix}
3 & 0 & 0 \\
0 & 4 & 0 \\
0 & 0 & 3
\end{pmatrix}

which is not an identity matrix? What have I not understood?

Thanks!

 

[kuruman]

What have I not understood?

Your method is correct. Check your implementation of it. You should put the radicals back in the ##S_x## and ##S_y## matrices where they belong before you add them.

 

[Jammy453]

Your method is correct. Check your implementation of it. You should put the radicals back in the ##S_x## and ##S_y## matrices where they belong before you add them.

I see where I went wrong now, thank you!