Vector model of atom. Hopefully easy question.

  1. 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.
     
  2. jcsd
  3. DrDu

    DrDu 4,115
    Science Advisor

    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.
     
  4. 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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