Hydrogen Atom Part 4: Solving the Radial Equation and finishing up

In this video I will finish solving the hydrogen atom by solving the radial equation that we found in part 1.

In the next video we will write some of the wavefunctions

My name is Nick Heumann, I am a recently graduated physicist. I love to teach physics, so I decided to give YouTube a try. English is not my first language, but I hope that you can understand me well enough regardless.
▬ Contents of this video ▬▬▬▬▬▬▬▬▬▬
00:00:00 How to begin
00:01:30 Explaining the first change of variable
00:08:00 Rearranging the equation
00:09:50 Substituting in the potential
00:12:00 cleaning up the notation
00:15:10 Looking for another change of variable
00:17:30 Defining rho_0
00:18:40 Determining the solution when rho is large
00:21:10 Determining the solution when rho is small
00:27:20 Looking for the rest of the solution (v)
00:28:00 Differentiating twice
00:33:50 Substituting back into the differential equation
00:37:50 Solving the resulting equation via power series
00:42:32 Changing the indexes
00:44:41 Deriving the recursion relation
00:49:30 Discovering the quantum number "n"
00:51:14 Determining the allowed energies
00:55:35 Identifying allowed values for "n", l and m
00:59:50 Writing down the actual solution to the radial equation