- #1

- 762

- 59

## Homework Statement

What is the commutation relation between the x and y components of angular momentum L = r X P

## Homework Equations

None.

## The Attempt at a Solution

I do r X p and get the angular momentum componants:

[tex]L_{x} = (-i \hbar) (y \frac{d}{dz} - z \frac{d}{dy})[/tex]

[tex]L_{y} = (-i \hbar) (z \frac{d}{dx} - x \frac{d}{dz})[/tex]

[tex]L_{z} = (-i \hbar) (x \frac{d}{dy} - y \frac{d}{dx})[/tex]

then when I attempt to put into the commutation relation [L

_{x},L

_{y}] it comes out very complicated.

My question:

I found a derivation BUT it has extra terms in it (circled in red)

Why are there 5 terms when there should only be 4 when multiplying out 2 brackets? It's important because those 2 extra terms enable the correct solution. Or have I missed something?

Thankyou for any help in advance.

Source of derivation: http://www2.ph.ed.ac.uk/~ldeldebb/docs/QM/lect8.pdf