Charmonium Mass Estimation: Trial Wavefunction for Variational Method

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Discussion Overview

The discussion revolves around estimating the mass of charmonium using trial wavefunctions within the variational method. Participants focus on the confinement aspect of the potential, while some express concerns about ignoring other effects such as Coulombic interactions and relativistic factors.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant seeks suggestions for trial wavefunctions to estimate charmonium mass, specifically focusing on confinement without considering Coulombic effects.
  • Another participant suggests common potentials, including the Cornell potential and alternatives that incorporate logarithmic terms.
  • A participant expresses interest in deriving an equation for ground state energy in terms of mass, proposing an exponential trial wavefunction with a polynomial in r.
  • One participant critiques the approach of focusing solely on the confining part of the potential, arguing that the short-distance part is crucial for determining the ground state and suggests using a potential that includes a Coulombic component.

Areas of Agreement / Disagreement

Participants exhibit disagreement regarding the appropriateness of focusing solely on the confining aspect of the potential, with some advocating for a more comprehensive approach that includes Coulombic effects.

Contextual Notes

Participants highlight the importance of considering both short-distance and long-distance behaviors of the potential, indicating that the choice of trial wavefunction may significantly affect the estimation process.

Who May Find This Useful

This discussion may be of interest to those studying quantum mechanics, particularly in the context of potential models and variational methods in particle physics.

starbud27
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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??!
 
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I think common potentials are either the "Cornell potential" V=-g^2/r+ar or
V=g^2/r+a ln(r).
 


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!
 


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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