(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I have the following expressions for angular momentum components: [itex]L_1 = x_2\frac{\partial}{\partial x_3} - x_3\frac{\partial}{\partial x_2}[/itex], [itex]L_2 = x_3\frac{\partial}{\partial x_1} - x_1\frac{\partial}{\partial x_3}[/itex], [itex]L_3 = x_1\frac{\partial}{\partial x_2} - x_2\frac{\partial}{\partial x_1}[/itex], and I simply need to work out [itex]L^2 = L_1^2 + L_2^2 + L_3^2[/itex].

2. Relevant equations

N/A

3. The attempt at a solution

Well, the way I expand it gives [tex]L_1^2 = (x_2\frac{\partial}{\partial x_3} - x_3\frac{\partial}{\partial x_2})(x_2\frac{\partial}{\partial x_3} - x_3\frac{\partial}{\partial x_2}) = x_2\frac{\partial}{\partial x_3}x_2\frac{\partial}{\partial x_3} - x_2\frac{\partial}{\partial x_3}x_3\frac{\partial}{\partial x_2} - x_3\frac{\partial}{\partial x_2}x_2\frac{\partial}{\partial x_3} + x_3\frac{\partial}{\partial x_2}x_3\frac{\partial}{\partial x_2} = -x_2\frac{\partial}{\partial x_2} - x_3\frac{\partial}{\partial x_3},[/tex] and similarly [tex]L_2^2 = -x_1\frac{\partial}{\partial x_1} - x_3\frac{\partial}{\partial x_3}[/tex] and [tex]L_3^2 = -x_1\frac{\partial}{\partial x_1} - x_2\frac{\partial}{\partial x_2},[/tex] so that [tex]L^2 = -2x_1\frac{\partial}{\partial x_1} - 2x_2\frac{\partial}{\partial x_2} - 2x_3\frac{\partial}{\partial x_3}[/tex] But this is not the expression for [itex]L^2[/itex] that I'm supposed to get! So I must be doing something wrong. Can anyone help?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: A calculation involving differential operators

**Physics Forums | Science Articles, Homework Help, Discussion**