# Homework Help: QM: commutator 2D particle magnetic field

1. Nov 1, 2015

### zhaos

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

2. Relevant equations
In the equation of the page (unlabeled), we have
$$\left[A_x\frac{\partial}{\partial y} - \frac{\partial}{\partial y}A_x + \frac{\partial}{\partial x}A_y - A_y\frac{\partial}{\partial x}\right]\psi(x)\\ = \left[- \frac{\partial A_x}{\partial y}+ \frac{\partial A_y}{\partial x}\right]\psi(x)$$

3. The attempt at a solution
Why do the first and fourth terms cancel out? Is it to do with the circular motion of the charged particle in the magnetic field?

2. Nov 1, 2015

### blue_leaf77

For example, for the second term in the first line of your equation
$$- \frac{\partial}{\partial y}(A_x \psi(x)) = - A_x \frac{\partial \psi(x)}{\partial y} - \psi(x)\frac{\partial A_x}{\partial y}$$
The first term of the right hand side in the above equation will cancel with the first term in

3. Nov 1, 2015

### zhaos

Oh. That makes it clear. Thank you.