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Orbital angular momentum and powers of k

  1. Apr 7, 2013 #1
    Hi guys,
    I have a question which is probably stupid. I am studying angular momentum and I have found almost everywhere that, if we have orbital angular momentum higher than [itex]\ell=0[/itex] then it brings powers of the momentum of the system like [itex]k^\ell[/itex]. What is the reason of that? Can someone suggest a book where I can find it or something?

    Thank you
  2. jcsd
  3. Apr 7, 2013 #2
    I may be able to help but I need to know where this is coming from. You say this appears in a few books, can you name one so I can check what it says?
  4. Apr 8, 2013 #3
    You can find it, for example, in Weinberg - Lectures on Quantum Mechanics, in the chapter on Shallow Bound States, when he talks about the request for the state to be in S-wave in order to avoid suppression by factors [itex]k^\ell[/itex].
  5. Apr 9, 2013 #4
    It comes out by solving the radial part of wave eqn which contains the factor of l(l+1),there we use
    ρ=kr as the variable and in some simplification with potential,the solutions are of the form (ρl)+(1/ρl+1),second part is rejected for finiteness near the origin which does give kl type term.All quantum mechanics books containing scattering theory deals with it.
  6. Apr 9, 2013 #5
    Ok, thank you very much. I'll definitely take a look at that!
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