Quantum numbers in wikipedia's table

[fluidistic]

I don't understand why there are 2 dashed values in this table: http://en.wikipedia.org/wiki/Quantum_number#Quantum_numbers_with_spin-orbit_interaction.
I have that j=l+s,l+s-1,...,|l-s|. So let's take #1 of the table.
They give l=1 and we know that s=1/2. Thus j=l+s=3/2 or j=l-s=1/2. Why is l-s=1/2 dashed?!
The same question appears for #6.

 

[dextercioby]

It violates the rule from

The projection of the total angular momentum along a specified axis (mj = −j, −j + 1, …, j), which is analogous to m, and satisfies mj = mℓ + ms where |mℓ + ms| < j.

(also on the webpage you referenced).

 

[fluidistic]

It violates the rule from

The projection of the total angular momentum along a specified axis (mj = −j, −j + 1, …, j), which is analogous to m, and satisfies mj = mℓ + ms where |mℓ + ms| < j.

(also on the webpage you referenced).

Ok thank you. But I am confused. They say that mj goes from -j to j via integers. And then that the modulus of mj must be strictly smaller than j. Thus how can mj be worth j?

 

[fluidistic]

Ah nevermind, I understood. In that example, if j=1/2, you can't get an mj=3/2 because if j=1/2 then mj=-1/2 or 1/2.
But shouldn't they say |m_l+m_s| =|m_j| \leq j rather than < j?

 

[dextercioby]

Yes, now that I think about it, it should include equality, too. Typo, maybe.

 

[fluidistic]

Ok thank you very much!