# Quantum numbers in wikipedia's table

1. Dec 1, 2011

### 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.

2. Dec 1, 2011

### 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).

3. Dec 1, 2011

### fluidistic

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?

4. Dec 1, 2011

### 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?

5. Dec 2, 2011

### dextercioby

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

6. Dec 2, 2011

### fluidistic

Ok thank you very much!