I’ve seen the uncertainty principle used to calculate the ground state energy for things like hydrogen and the harmonic oscillator, but can this be done for the Yukawa potential where you have an exponential?
Links for context:
1. https://en.wikipedia.org/wiki/Yukawa_potential
2. https://en.wikipedia.org/wiki/Yukawa_interaction#Classical_potential
I'm working on my BSc right now and I'm solving the energies of 2 nucleon systems (so basically just deuteron) by treating them as non-relativistic two...
Homework Statement
The photon is normally assumed to have zero rest mass. If the photon did have a tiny mass, this would alter the potential energy the electron feels in the hydrogen atom (due to the Coulomb interaction with the proton). The potential then becomes yukawa potential...
Hello there!
I was doing my Gravitation problems and I found this problem that I'm unable to solve.
Yukawa's theory for nuclear forces states that the potential energy corresponding to the attraction force produced by a proton and a neutron is:
U(r) = \frac{k}{r}e^{-\alpha r},\ k<0,\ \alpha > 0...
Homework Statement
a)Show that the yukawa potential is a valid static-field euation
b)Show this solution also works
Homework Equations
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}...