Help with Research: Ideas for Extending Problem Results

[drelek]

Hello all,

I would like to start by saying that i new to this website and am not sure if this the exact category i should be posting this question in.

I recently began studying a problem which can be best described as a variation on the hydrogen atom problem, where the electrostatic Coulombic force is replaced by a non linear spring type force. I believe that i will not have trouble in solving this problem and am currently trying to think of ways that i could extend this problem to make it more complex and apply to the real world more. Though the use of a non-linar spring type for may seem quite artificial as it is clear protons and electrons are not help together by string, i assure you that it is not as artificial as it may seem.

An example of a physical problem that does involve nonlinear 'spring type' forces and (ideally) infinitely many degrees of freedom is that of vibrations of a crystal lattice wherein one pretends for simplicity that the lattice extends infinitely far in all directions filling up space. The forces between the atoms or molecules of the lattice could be regarded realistically as nonlinear spring forces of the type you are studying. In fact most textbooks simplify things by assuming they are linear springs but this is an approximation. I just mention this to point out that this idea is not as un-applicable as one might think.

Any ideas of how i could extend the results of this project would be greatly appreciated.

Thank you for taking the time to read this email and have a nice day.

 

[fzero]

The addition of a linear potential to the Coulomb potential is known as the Cornell potential, and is useful in the study of bound states of heavy quarks: http://en.wikipedia.org/wiki/Quarkonium#QCD_and_quarkonia. There are no useful references on that page, but you might find some if you search for references on non-relativistic QCD (NRQCD).

 

[drelek]

thank you very much for your idea fzero, if anyone else has any ideas they would be greatly appreciated.

Thank you for your time