# Raising and lowering operators

1. May 5, 2017

### davon806

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

1.1st circle on the left : where did I miss a minus sign?
2. How to show that the last term is equal to 1?

Thanks!

2. May 5, 2017

### TSny

I don't think you missed a minus sign here.
You'll have to see if it is, in fact, equal to 1.

You could try expanding the two exponentials in your question-mark expression and see if you can simplify it. Think about what happens when you act on the ground state with powers of a followed by powers of a.

3. May 5, 2017

### davon806

Thanks, after expanding the exponential I recover the minus sign.

4. May 5, 2017

OK, good.