Minimizing total vs potential energy

Question

In class, we have found the minimum distance between two molecules by minimizing Lennard-Jones potential. We have also approximated the distance of a ground state electron from the nucleus using the uncertainty principle and minimizing total energy. This method can be found in the Feynman Lectures and is detailed in the body of this post.

My question is why do we minimize only the potential energy in the Lennard-Jones example, while we minimize the total energy in Feynman's approach?

Answer 1

When minimizing the Lennard Jones potential, you're working in the rest frame of the molecules, so the kinetic energy is zero. Therefore, minimizing the potential energy is the same thing as minimizing the total energy.