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Vector model of atom. Hopefully easy question. 
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#1
Sep713, 04:43 PM

P: 310

In system with one electron total angular moment vector ##\vec{j}## is just:
[tex]\vec{j}=\vec{l}+\vec{s}[/tex] http://selfstudy.in/MscPhysics/BScVectorModelOfAtom.pdf In page 3 author draw a triangle. Intensities of the vectors are ##\vec{l}=\sqrt{l(l+1)}\hbar##, ##\vec{s}=\sqrt{s(s+1)}\hbar##, ##\vec{j}=\sqrt{j(j+1)}\hbar## And then from nowhere ##j=l+s## or ##j=ls##. Could you please explain me that! Tnx. 


#2
Sep813, 03:12 AM

Sci Advisor
P: 3,560

These are maximal and minimal possible values, respectively. If you add two vectors, the length of the sum will always lie between these two extremal values.



#3
Sep813, 07:02 AM

P: 310

But if I look this intensity formulas
[tex]\vec{l}+\vec{s}\neq \vec{j}_{for j=l+s}[/tex] Right? 


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