A question on momenta of electrons

[rushil]

Is there any special significance of the fact that $$\vec{L}$$ and $$\vec{S}$$ of an electron are in-phase or out-of-phase at all times?

i.e. is there any special physical significance of the fact that

(i) $$| \vec{J} | = | \vec{L} | + | \vec{S} |$$
(ii) $$| \vec{J} | = | \vec{L} | - | \vec{S} |$$
I am referring to magnitudes above!
Also, is there any significance of the fact that $$\vec{L}$$ and $$\vec{S}$$ are NOT in phase at any time?
We are obviously assuming simple electronic configurations!

 

[Physics Monkey]

The total angular momentum is always $$\vec{J} = \vec{L} + \vec{S}$$, the rule you refer to has to do with the allowed values of the $$J^2$$ quantum number.

 

[rushil]

Can you please explain a bit more!

 

[Physics Monkey]

I'm afraid I don't have anymore time at the moment. Someone else will probably be able to help you further, but if no one else answers, I will try to expand on my answer some more later. In the meantime, have a look at this: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/vecmod.html