- #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?