Do Angular Momentum Components Commute with Nabla Squared and r Squared?

[SunGod87]

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:
<br /> [L_x, \nabla^2] = L_x \nabla^2 - \nabla^2 L_x<br />

The Attempt at a Solution

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

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

How can I simplify these?

 

[Hurkyl]

If you have no better ideas, then why not rewrite \nabla^2, just like you did with L_x?

 

[snapback]

after rewriting \nabla^2 as Hurkyl suggested, you should apply the commutator (it is also an operator) to a differentiable function f(x,y,z) and see whether the differentiation rules (e.g.differentiation of a product) make the equation look simplier.