- #1

SunGod87

- 30

- 0

## Homework Statement

Show the three components of angular momentum: L_x, L_y and L_z commute with nabla^2 and r^2 = x^2 + y^2 = z^2

## Homework Equations

[A, B] = AB - BA

For example:

[itex]

[L_x, \nabla^2] = L_x \nabla^2 - \nabla^2 L_x

[/itex]

## The Attempt at a Solution

[itex]

L_x \nabla^2 = -i\hbar(y\frac{\partial}{\partial z} \nabla^2 - z \frac{\partial}{\partial y}\nabla^2)

[/itex]

[itex]

\nabla^2 L_x = -i\hbar\nabla^2(y\frac{\partial}{\partial z} - z \frac{\partial}{\partial y})

[/itex]

How can I simplify these?