For spin 1, the states are |1>, |-1> and |0>(adsbygoogle = window.adsbygoogle || []).push({});

These are written as:

|1> = column matrix[1 0 0]

|0> = column matrix [0 1 0]

|-1> = column matrix [0 0 1]

I need to find the 3 x 3 matrices for S(+) and S(-) which operate on these kets to give the correct answers eg.

S(-)|1> = sqrt(2)*h(bar)*|0>

I had tried getting linear eqns from the following:

[a b c] * [1] = h(bar)*sqrt(2)* [0]

[d e f] [0] [1]

[g h i] [0] [0]

but i just get

a + 0 + 0 = 0

d + 0 + 0 = 1* h(bar) * sqrt(2)

g + 0 + 0 = 0

This doesn't look remotely useful... I know the lowering operator is:

[ 0 0 0 ]

[sqrt(2) 0 0 ]

[ 0 sqrt(2) 0 ]

But how do I get there?

Cheers for any help

Philip

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# How to find S(+) 3 x 3 matrix?

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