- #1
philip041
- 107
- 0
For spin 1, the states are |1>, |-1> and |0>
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
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