Raising and Lowering Operators

[dFrankCalc]

I am working on a homework problem from quantum mechanics. In order to solve the problem I need to derive the raising and lowering operators.

In order to to this I did the following:

S+operator = <1,i | S+operator | 1,j > where i = 1, 0, -1 with i = 1 corresponding to row one etc. I let j = 1, 0, -1 , corresponding to the columns where j = 1 is column one.

I was able to calculate every thing the same as what the book has i.e.
S+operator =hbar*sqrt(2)*[0,1,0;0,0,1; 0,0,0] except I am off by a factor of sqrt(2). Where does this factor come from?



DFrankCalc

 

[Born2bwire]

Normalization probably. Are the eigenstates of your operator normalized if needed?

 

[dFrankCalc]

The Sz eigen states that I used to get S+ are properly normalized.