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Vector model of atom. Hopefully easy question.

by LagrangeEuler
Tags: atom, model, vector
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LagrangeEuler
#1
Sep7-13, 04:43 PM
P: 316
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.
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DrDu
#2
Sep8-13, 03:12 AM
Sci Advisor
P: 3,630
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.
LagrangeEuler
#3
Sep8-13, 07:02 AM
P: 316
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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