In scattering theory, P wave means $l=1$, where $l$ is the azimuthal quantum number. However, what does P wave mean when referring to particle states? For example, in this paper (arXiv link), the authors are talking about P-wave charmonia states. What does that mean?

More specifically, I understand that in some sort of potential model, solved using Schroedinger equation for example, there will be states that may be labeled by $n$=something, $l=1$. But here, the article says P-''wave'' charmonia! What is this wave?

  • $\begingroup$ They are talking about charmonium which is the meson $c\bar{c}$, see this Wikipedia article on the J/$\psi$ meson (this is mentioned in the opening paragraph of the linked paper as well). $\endgroup$
    – Kyle Kanos
    Sep 4, 2014 at 14:17
  • $\begingroup$ Kyle Kanos - thanks for the edit and yes, they are talking about charmonium. I have read that wiki article, but that doesn't answer the wave part. Thanks anyways. $\endgroup$ Sep 4, 2014 at 14:20
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    $\begingroup$ Kyle Kanos - I'm not too sure about that. In non-relativistic treatments, one does talk about the wave function, but in general in particle Physics, single particle wavefunctions are problematic aren't they? (e.g. in the simple Klein Gordon, or Dirac equation solutions etc.) So, wave standing for wavefunction does not look right to me, especially since notation would be general and not specific to NR. But nevertheless, thanks for your participation in this. You certainly improved my question. $\endgroup$ Sep 4, 2014 at 14:39
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    $\begingroup$ Recall that the s, p, d, f naming scheme originally came from atomic spectroscopy not from scattering theory. It applies just fine to bound systems such as charmonium without any need to talk about wave functions. The state has such-and-so angular momentum. The appellation "p-wave" is just habit. $\endgroup$ Sep 4, 2014 at 14:59
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    $\begingroup$ Related question on Astronomy: astronomy.stackexchange.com/q/6257 $\endgroup$
    – HDE 226868
    Apr 1, 2015 at 18:49

1 Answer 1


The states of charmonium are treated as bound states of a charmed quark ($c$) and its anti-quark ($\bar{c}$). Since the binding energy of the $c-\bar{c}$ system is relatively small, compared to the rest energy of the charmed quarks, it is a reasonable starting point to analyze the states using the non-relativistic Schroedinger equation with a potential derived from QCD (Coulomb-like at short distances, linear at large distances to keep the quarks confined). As already commented on, the s, p, d, f naming scheme for states of definite orbital angular momentum goes back to the days of atomic spectroscopy -- it was also used in the study of the nucleon-nucleon system (both for the deuteron and for the scattering states).


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