Charmonium Mass Estimation: Trial Wavefunction for Variational Method

[starbud27]

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??!

 

[Meir Achuz]

I think common potentials are either the "Cornell potential" V=-g^2/r+ar or
V=g^2/r+a ln(r).

 

[starbud27]

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!

 

[Vanadium 50]

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.