# Proof of how [a+,[a+,a]]=0

1. Sep 30, 2009

### meanyack

1. The problem statement, all variables and given/known data
Actually the question is two long and I'll be done if I can show that
[a+,[a+, a]=0 and similarly
[a,[a+, a]=0
where a+ is the raising and a is the lowering ladder operator in quantum oscillator.

2. Relevant equations
I tried the formulas
[A,[B,C]]= -[C,[A,B]] -[B,[C,A]] and
a$$\psi$$n=$$\sqrt{n}$$$$\psi$$n-1
a+$$\psi$$n=$$\sqrt{n+1}$$$$\psi$$n+1
3. The attempt at a solution

2. Sep 30, 2009

### keniwas

The Jacobi Identity is [A,[B,C]] = [[A,B],C] + [B,[A,C]]

3. Sep 30, 2009

### meanyack

why can't I see a button "delete topic" because this is the wrong topic, the original one is the other one

Last edited: Sep 30, 2009