- #1

Hart

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## Homework Statement

The Yukawa potential is given by:

[tex] V_{\gamma}(r) = -\frac{q^{2}}{4\pi \epsilon_{0}r}e^{-\gamma r}[/tex]

Where [tex]\gamma[/tex] is a constant. This describes a screened Coulomb potential.

I. Sketch the radial dependance of this potential.

II. State the radial Schodinger equation for this potential.

III. Assume that [itex]\gamma[/itex] is a small parameter. Use first order perturbation theory to estimate the energy shift of the ground state of the hydrogen atom when the Coulomb potential is replaced by the Yukawa potential. Hint: The perturbation is:

[tex]\omega = V_{\gamma}-V_{0}[/tex].

## Homework Equations

Within the question statement / answers.

## The Attempt at a Solution

I don’t seem to be able to find much useful information about this potential which I can understand and/or use to try and answer this question.

I. Obviously I know that it’s hard to show what it looks like over these forums, but any description of what it looks like would be great.. I don’t know.

II. Help and advice needed!

III. Again, help and advice needed!

.. sorry I don't have really any input at the moment, but I really don't get what's going on here and havn't been able to find much info elsewhere.