A thin, metal wire is bent into a circular loop of radius R $=1\mathrm{.}0$ nm$,$ and a single electron is place on the wire. The metal loop is at a constant potential. This is essentially a particle in a $1-$dimensional box, but with different boundary conditions. The boundary conditions are like those used to describe the orbital motion of an electron around a hydrogen atom. a$)$ Solve for the energy eigenvalues of the electron on the loop. Hint: Start by writing down the standing wave conditions appropriate for this topology. b$)$ How many states are there for any particular energy eigenstate? That is$,$ what is the degeneracy of each energy level? Hint: do not forget about the electron$$s spin.