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Quantum Numbers

  1. Jan 18, 2008 #1
    [SOLVED] Quantum Numbers

    What is the difference between using J and l for quantum numbers? I have some lecture notes that aren't fully explained. It was talking about rotational transitions for diatomic molecules, and said the energy of a photon going from level J to level J-1 is [tex]\frac{Jh^2}{4\pi^2\mu(r^2)}[/tex]. Now, I remember from my quantum module last year, that [tex]E_{rot}=\frac{L^2}{2I}=\frac{l(l+1)h^2}{8\pi^2\mu(r^2)}[/tex]. I can see the resemblance between the two equations, but I just can't figure out the link between J and l!
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  3. Jan 18, 2008 #2
    "l" quantum is number is specifically used to describe angular momentum.

    "j" can either describe angular momentum or spin.
  4. Jan 18, 2008 #3
    Yes, I found those descriptions online, but it doesn't help me with the link between them - we were told that J was the rotational quantum number of the upper level. If these two equations ARE the same, that means that 2J=l(l+1) - is this true? And if so, what are the steps to prove it?
  5. Jan 18, 2008 #4


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    Many different notations and conventions are used. So you must look up the definition given in your difference.

    But you have not been careful here, [tex]\frac{Jh^2}{4\pi^2\mu(r^2)}[/tex] is the energy difference of states with QM# J and J-1, and the level energies are given according to: [tex]E_{rot}=\frac{{\vec{J}}^2}{2I}=\frac{J(J+1)h^2}{8\pi^2\mu( r^2)}[/tex]

    So you must evaluate [tex]E_J - E_{J-1}[/tex]
    Last edited: Jan 18, 2008
  6. Jan 18, 2008 #5
    I hadn't realised it, but it's so simple when you put it like that. Thanks, that's helped a lot!
  7. Jan 18, 2008 #6


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    hehe :biggrin:
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