Vector model of atom. Hopefully easy question.

  • #1
653
15
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=l-s##. Could you please explain me that! Tnx.
 

Answers and Replies

  • #2
DrDu
Science Advisor
6,145
817
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
653
15
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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