Where did I miss a minus sign?

[davon806]

Homework Statement

Homework Equations

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!

 

[TSny]

1.1st circle on the left : where did I miss a minus sign?

I don't think you missed a minus sign here.

How to show that the last term is equal to 1?

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.

 

[davon806]

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.

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

 

[TSny]

OK, good.