# Homework Help: Yukawa potential and the Klein Gordon

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1. Mar 15, 2015

### unscientific

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

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

2. Relevant equations

3. The attempt at a solution

Part (a)

Using the relation given, I got

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

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

$$LHS = \left( E^2 - p^2 - m^2 \right)\phi$$

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?

2. Mar 15, 2015