Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Muonic hydrogen, change in potential of the muon.

  1. Jun 23, 2011 #1


    User Avatar

    1. The problem statement, all variables and given/known data

    Taking the proton to be a uniformly charged sphere of radius 1 fm, find an
    expression for the change in potential experienced by the muon as compared with that
    in the case of a point-like proton. Use first order perturbation theory to calculate the
    ground-state energy shift in muonic hydrogen

    2. Relevant equations


    3. The attempt at a solution

    The electric field due to a uniformly charged sphere is exactly the same as the field due to a point charge of the region outside the sphere (by a simple application of gauss's law). For this reason I see no need for the potential to change. What am I missing?
  2. jcsd
  3. Jun 23, 2011 #2


    User Avatar
    Science Advisor

    What you say is true - the potential outside of the proton is unchanged. However, the potential inside the proton is different in the two cases. Since the wave function at the origin is non-zero, there is some finite probability for the muon to be found inside the proton. So you can take the standard 1S solution as the unperturbed state, and apply a perturbation which is a difference between the potential of a point charge and the potential of a sphere. The perturbation is only non-zero inside the proton.
  4. Jun 23, 2011 #3


    User Avatar

    Thanks. That makes sense.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook