I am currently working through Griffiths' textbook on quantum mechanics. The hydrogen atom was first modelled as a one body system with the proton fixed at the origin. In this case the potential was given by Coulomb's law,(adsbygoogle = window.adsbygoogle || []).push({});

[tex]V(r) = -\frac{e^2}{4\pi\epsilon_0}\frac{1}{r} \ ,[/tex]

whereris the radial coordinate.

This potential is easy to visualise as a "potential well" -- at least in two dimensions -- with the proton at the centre with V=-∞ and then the potential approaching 0 as r goes to ∞.

However, the hydrogen atom is then reconsidered as a multi body problem with the motion of the proton now accounted for. The positions of the particles are given byrand_{1}r, and I understand the change into new coordinates: the separation distance_{2}rand the centre of massR.

My question is this: how can the potential

[tex]V(\vec{r}_1,\vec{r}_2) = V(\vec{r}_1-\vec{r}_2) = V(\vec{r}) = V(|\vec{r}|) = -\frac{e^2}{4\pi\epsilon_0}\frac{1}{r} [/tex]

now be visualised as a potential well. Can this only be done in some kind of 2n-dimensional "configuration space" (where n is the number of space dimensions) of tuples

[tex](\vec{r}_1,\vec{r}_2) \ ?[/tex]

Also, what is the interpretation of a general multi body potential

[tex]V = V(t,\vec{r}_1,\vec{r}_2,\ldots,\vec{r}_m) \ ?[/tex]

Is this thetotalpotential energy of the system at timetwhen particle 1 is at positionr, particle 2 is at position_{1}rand so on?_{2}

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Visualising Potential Wells in Two Body Systems

Loading...

Similar Threads for Visualising Potential Wells |
---|

I Tunneling through a finite potential barrier |

A Vacuum in QFT: Fock space or effective potential? |

I Probabilities Associated with Sudden Changes in Potential |

I Lho potential |

I About the strength of a perturbing potential |

**Physics Forums | Science Articles, Homework Help, Discussion**