Angular Momentum Equations

[jg370]

1. The problem statement, all variables and given/known data
In my study of Quantum Mechanics, I am using Introduction to Quantum Mechanics by David J. Griffiths. So far I have done quite well. However, as I come to the section on Angular Momentum, I need help to get further.

2. Relevant equations
Classically, the angular momentum of a particle is given by:

\mathbf{L = r\times p }

This is all good. But this is followed by component form of the above equation as:

L_x = yp_z-zp_y, L_y = zp_x-xp_z, L_z = xp_y-yp_z

I am curious how L_x, L_y , L_x are mathematically derived

3. The attempt at a solution

I have look at other textbooks and various posting on internet but I have not been able to find anything to help me with. Hopefully, someone will suggest some thing.

Thanks

[D H]

Let \mathbf r = x\hat x + y\hat y + z \hat z and [ltex]\mathbf p = p_x \hat x + p_y \hat y + p_z \hat z[/itex]. What ls \mathbf L = \mathbf r \times \mathbf p?

[ideasrule]

By the way, that definition is just part of classical mechanics. It's not unique to quantum mechanics.