# mutual orientation

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NoetherTheorem
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J-value may be calculated according to the formula:

J = L+S, …, |L-S|

L = 1, S = 1, J = 1+1 = 2

L = 1, S = 0, J = 1 + 0 = 1

L= 1, S = 1, J = |1-1| = 0

For J = 2, L and S are parallel and point in the same direction. It’s the most disadvantageous system, the highest energy.

If J = 1, L and S are perpendicular to each other. Only one of them is thus fruitfully projected on the z-axis.

Antiparallelity of L and S onsets when J = 0. Because the total angular momentum of the electron shell is minimum, this is the ground state with the lowest energy.

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