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Quantum numbers in wikipedia's table

  1. Dec 1, 2011 #1

    fluidistic

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    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 [itex]j=l+s,l+s-1,...,|l-s|[/itex]. So let's take #1 of the table.
    They give l=1 and we know that [itex]s=1/2[/itex]. Thus [itex]j=l+s=3/2[/itex] or [itex]j=l-s=1/2[/itex]. Why is l-s=1/2 dashed?!
    The same question appears for #6.
     
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  3. Dec 1, 2011 #2

    dextercioby

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    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).
     
  4. Dec 1, 2011 #3

    fluidistic

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    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?
     
  5. Dec 1, 2011 #4

    fluidistic

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    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 [itex]|m_l+m_s| =|m_j| \leq j[/itex] rather than < j?
     
  6. Dec 2, 2011 #5

    dextercioby

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    Yes, now that I think about it, it should include equality, too. Typo, maybe.
     
  7. Dec 2, 2011 #6

    fluidistic

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    Ok thank you very much!
     
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