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Charmonium: estimating the mass - trial wavefunction for use in variational method?

  1. Nov 16, 2009 #1
    Charmonium: estimating the mass - trial wavefunction for use in variational method??

    Hi,

    I need any suggestions of trial wavefunctions I can use to find an order of magnitude estimate for the mass of charmonium in the variational method.

    I am ignoring coulombic effects (and relativistic) - just interested in the confinement aspect of the potential at the moment..

    Can anybody help??!
     
  2. jcsd
  3. Nov 18, 2009 #2

    clem

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    Re: Charmonium: estimating the mass - trial wavefunction for use in variational metho

    I think common potentials are either the "Cornell potential" V=-g^2/r+ar or
    V=g^2/r+a ln(r).
     
  4. Nov 18, 2009 #3
    Re: Charmonium: estimating the mass - trial wavefunction for use in variational metho

    Thanks for the suggestion! But yeah essentially I want to get an equation for the ground state energy in terms of the mass and then use known energies to make estimates for the mass... How can I go about this (without using computational methods..) - i thought using the variational method with a trial wavefunction - maybe an exponential one with a polynomial in r?? Any suggestions?!

    If not... what are some of the general features of the wavefunction for charmonium so I can at least have an idea of what i need it to be?

    Thanks!!!
     
  5. Nov 18, 2009 #4

    Vanadium 50

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    Re: Charmonium: estimating the mass - trial wavefunction for use in variational metho

    I think the idea of looking at just the confining part is a bad idea.

    The confining part is the long-distance part of the potential. If you want the ground state, that's the short-distance part.

    I would pick a potential that has a 1/r Coulombic part and some confining part, and use the Coulombic wavefunction as the trial wavefunction: because we know what that wavefunction is exactly.
     
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