Charmonium Mass Estimation: Trial Wavefunction for Variational Method

In summary, the individual is looking for suggestions on trial wavefunctions to use in order to estimate the mass of charmonium using the variational method. They are interested in the confinement aspect of the potential and plan to use a potential with a 1/r Coulombic part and a confining part. They also mention the possibility of using an exponential wavefunction with a polynomial in r.
  • #1
starbud27
2
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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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  • #2


I think common potentials are either the "Cornell potential" V=-g^2/r+ar or
V=g^2/r+a ln(r).
 
  • #3


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!
 
  • #4


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.
 

1. What is charmonium and why is it important?

Charmonium is a subatomic particle consisting of a charm quark and an anti-charm quark bound together by the strong nuclear force. It is important for studying the behavior of quarks and their interactions, as well as for understanding the structure of matter at a fundamental level.

2. What is the trial wavefunction for variational method and how does it relate to charmonium mass estimation?

The trial wavefunction for variational method is a mathematical function used to approximate the actual wavefunction of a particle. In the context of charmonium mass estimation, it is used to determine the mass of the charmonium particle by variational methods, which involve optimizing the trial wavefunction to obtain the most accurate result.

3. What factors influence the accuracy of charmonium mass estimation using the trial wavefunction for variational method?

The accuracy of charmonium mass estimation using the trial wavefunction for variational method depends on various factors such as the choice of the trial wavefunction, the number of parameters used in the wavefunction, and the method used for optimization. In addition, the accuracy can also be affected by the precision of the input data and the computational resources available.

4. How does the variational method compare to other methods for estimating charmonium mass?

The variational method is one of the most commonly used methods for estimating the mass of charmonium. It is a powerful tool because it allows for the optimization of the trial wavefunction, which can lead to more accurate results. However, other methods such as lattice QCD and sum rule methods can also be used for charmonium mass estimation and may provide complementary insights.

5. What are some current challenges in charmonium mass estimation using the trial wavefunction for variational method?

One of the main challenges in charmonium mass estimation using the trial wavefunction for variational method is the complexity of the calculations involved. It requires a significant amount of computational resources and can be time-consuming. Additionally, there is still ongoing research to improve the accuracy of the trial wavefunction and optimization methods for more precise results. Another challenge is the lack of experimental data for certain charmonium states, which can make it difficult to validate the results obtained through this method.

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