Energy eigenstates of hydrogen
PROFESSOR: Solutions can be organized. One way to do it, it's not the standard way, is with plotting n here and l here, and you have 0, 1, 2, 3, 1, 2, 3. You have all this points. Remember, every point this allowed. Every integer combination is allowed. All those are energy levels of the hydrogen atom, but now you can see that this point, when both are 0, corresponds to n equal to 1. Because if n and l are 0, n is equal to 1, and there's just one solution with n equal to 1. These two points here, when l is equal to 1 and n equals 0, with n is equal 1 and l equals 0, represent the two possibilities that realize n equals to 2. n equals to 2 is realized by having 1 and 0 or 1 and 0, two values. Similarly, there are three things with n equal to 3, four things-- my graph is not that great-- with n equal to 4, and more and more states. So for each n you have that n plus l is equal to n minus 1. And l can never exceed n minus 1, and that's physically quite something ...