# Effective Potential

1. Jul 26, 2004

### hiphys

Hi, May I ask you some questions on effective potential ?
I've heard about Krammer potential ? Exactly, what is it ?
Coulomb potential can be replaced by effective potential in some classical theory situation ?
Now, my project is about the approximation of effective potential in short range and high temperature. I wonder if we have the fomula of effective potential and can we find the exact value of it with finite distance and temperature ? Can you help me ?
My English is not good,but I hope you can get it.Thanks a lot.

2. Jul 26, 2004

### JohnDubYa

I assume it can take on many different meanings. For one, an effective potential replaces singular behavior with finite behavior, which better mimics the real-world potential when applying numerical analysis.

An example is the one-dimensional hydrogen atom. To model the atom, the singularity at x = 0 is replaced with an effective potential having a finite well depth. (Then the depth of the well is increased to mimic the singularity.)

Also, an effective potential could be the one-dimensional version of a 3-dimensional well, removing the angular dependence of the solution.

Finally, some of the terms in the Hamiltonian look like they are part of the potential energy function, but are in fact remnants of the kinetic energy function. The combination of the potential energy function and the kinetic energy remnant is often called an effective potential.

It could mean a lot of things, I suppose.

Last edited: Jul 26, 2004
3. Jul 27, 2004

### hiphys

Thanks,John.
We can reduce a quantum system of two particles with Coulomb interaction to that of a particle in central potential by using reduced mass.By that way, we got effective potential ,is it right ?
Can we have the exact value of this potential ?
In my documents, I have the fomula of effective potential : V(r).It contents a spherical Coulomb function Fl.I can't find the form of this function.I got stuck here.I can't find the value of effective potential.
Can you show me the definite form of Fl ?
Thanks again !

Last edited: Jul 27, 2004