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Yukawa potential and the Klein Gordon

  • #1
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Homework Statement



a)Show that the yukawa potential is a valid static-field euation
b)Show this solution also works

kleingordon1.png


Homework Equations




The Attempt at a Solution



Part (a)

Using the relation given, I got

[tex]LHS = \frac{e^{-\mu r}}{r} \left[ (m^2 - \mu^2) - \frac{2\mu}{r} - \frac{2}{r^2} \right] [/tex]

So for LHS = RHS = 0, it means that ##m = \mu = -\frac{1}{r}##, so the wavefunction is ##\phi = \frac{e}{r}##.

What does this mean?

Part (b)

Using the relation given, I got

[tex] LHS = \left( E^2 - p^2 - m^2 \right)\phi [/tex]

For LHS = RHS = 0, it means that ## E^2 - p^2 = m^2##.

Does this mean that the particle must be on the mass shell? i.e. an external particle and not an internal (virtual) particle?


What are the physical interpretations of these?
 

Answers and Replies

  • #2
TSny
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