# Quantum Mechanics - Lowering Operator

## Homework Statement

let A be a lowering operator.

## Homework Equations

Show that A is a derivative respects to raising operator, A†,

A=d/dA†

## The Attempt at a Solution

I start by defining a function in term of A†, which is f(A†) and solve it using [A , f(A†)] but i get stuck after that. Can someone please explain briefly what i should do in the next step?

##A_+|n> = |n-1> \, , \, A_-|n+1> = |n> ## so
$$A_+\,A_-\, |n> = |n> \,\Rightarrow\,\left(A_+A_- + [A_+,A_-]\right)|n> = |n>$$

##A_+|n> = |n-1> \, , \, A_-|n+1> = |n> ## so
$$A_+\,A_-\, |n> = |n> \,\Rightarrow\,\left(A_+A_- + [A_+,A_-]\right)|n> = |n>$$

sorry, i dont quite understand. Mind to explain it?

## |n> = \Psi_n ## my English is very poor for this theme. ## \frac{d}{dA_+}\left(A_+A_-+1\right) ## is that you need.

strangerep