 All right, so our next task is to solve the radial equation for the hydrogen atom. And that's what we have here. Previously we solved by separating variables in the hydrogen atom shorting our equation that the radial PCD equation looks like this, these various derivatives of the radial component of the wave function, this capital R function. If I take these various derivatives and multiply them and add them with these other components, what I get is a constant that we've called minus alpha. By considering the angular component of the shorting our equation, we decided that the angular behavior is just like a rigid rotor, so we knew the solutions to that problem. And this alpha, the value of alpha turned out to be this collection of constants multiplied by a quantum number. And again, from what we know about rigid rotor, we know that the value of L could be any non-negative integer. So that's what we have. Here is this radial function. So if I think about how to solve this equation, the way we can start is, again, simplifying it a little bit, I'm going to multiply by R to get rid of some terms like this, and I'm going to divide by R squared to get rid of some terms like this. So if I do both of those things on both sides of this equation, and again I can do that the first time through by just amending this equation, I multiply by R and then divide by R squared. That fixes the first term. In the second term, dividing by R squared turns this R into a 1 over R, and if I multiply by capital R, in this term I can divide by R squared, multiply by R, and on the right side of the equation, multiply by R, divide by R squared. So if I rewrite this equation, and when I do that I'll insert this value of alpha, and I'll bring this whole term, the negative alpha, R over R squared term, bring that over to the left-hand side. If I rewrite that equation it'll look like minus H squared over 8 pi squared mass R squared, and then these derivatives of the function R that we're looking for. I'll take this term next, so this minus alpha becomes a plus alpha is H squared over 8 pi squared mass, divide by R squared, capital R times L and L plus 1. Now all I have left is the Coulomb term, minus Z E squared over 4 pi epsilon not R times capital R, and then if I subtract energy times R I must get 0. So there's the differential equation that we need to solve. With one slight twist we can't solve this differential equation unless we know what value of L we're solving it for. L can take on any of these values, 0, 1, 2, and so on, so if I rewrite this equation with an L equals 0 in it, so when L equals 0 that one's fairly convenient because this L times L plus 1 makes this whole second term go away, so my differential equation looks like constants times DDR, R squared, derivative of capital R with respect to R, second term goes away, I have the Coulomb term and energy times capital R, so that's a somewhat simplified differential equation for the special case where L equals 0. On the other hand if L equals 1 I have an entirely different differential equation to solve. So we're writing out those terms again. I've got the first term involving derivatives of my radial function. I now do need to include a term that has some L's in it and when L equals 1, 1 times 2 gives me a 2, so I have some constants just times the radial wave function itself to which I add the Coulomb term and the energy term, and again those must be summed to 0. So I could write out an infinite number of these equations, the point being the differential equation I have to solve when L equals 0, that's a different differential equation than the one I have to solve when L equals 1 or L equals 2 and so on. So I have now a whole family of differential equations to solve, one for each possible value of L, and that's what we'll do in the next video.