 All right, so finally at long last we're ready to put together the full, shorting our equation, I'm sorry, the full wave function for the hydrogen atom. So what we've managed to do so far is after separating the variables, after deciding that our wave function might be a product of a radial piece and an angular piece, one that depends on only r, one that depends on theta and phi. We discovered that that does indeed solve the shorting our equation. The angular piece was familiar to us from the rigid rotor, so it has the same form as the rigid rotor wave function. The radial piece after some work we decided was a normalization constant times some pieces that look like polynomials in r times a decaying exponential. The radial piece depends on these two quantum numbers n and l. The angular piece depends on the quantum numbers l and m. So let's summarize real quickly what we know about those quantum numbers. Again the value of n can be any non-negative integer, I'm sorry any positive integer, one, two, three and so on. The name for that quantity is the principal quantum number. The value of l we've seen can run from zero up to n minus one but cannot be larger than that. That one is called the angular momentum quantum number. And lastly m which we haven't talked about recently but has the same meaning as it does for rigid rotor wave function. We know from the rigid rotor that can range from negative l all the way up to positive l and that one we call the magnetic quantum number. So the next thing we'll do is write down the full form of the wave function which depends not only on l but also on n and m. So for any valid combinations of these quantum numbers n's and l's and m's we can write down one of these wave functions. So what I'll do next is I'll write down those wave functions for several values of n and l and m so we can see what they look like. So that collection of radial Schrodinger equation wave functions looks like this, clearly they can get very complicated. But the point is we can calculate all of them if we just know the equations for how to calculate the radial and the angular portion and we multiply them together. So if we look at these I'll just point out a few key features. Form one each one of these n, l, m wave functions has a normalization coefficient out front and those normalization coefficients are different in principle for every one of these wave functions. That's just whatever the value needs to be so the wave function becomes normalized. Also notice that the normalization coefficient itself always includes the z over a naught to the three halves term that's there primarily for unit reasons. The normalization coefficient needs to have units of one over length to the three halves so that the units of the wave function are appropriate. After the normalization coefficient in the radial portion of the wave function we may have some terms that look like z r over a naught or maybe z r over a naught raised to with some coefficients in front raised to some power and again that n in the denominator is that value of the constant in the denominator corresponds to this n value. The power it gets raised to corresponds to the l value. There's also some polynomial portion of the radial part of the wave function that might be relatively simple. It might be relatively complex or it might be in some cases invisible because you're just multiplying by one and again that's the generalized Laguerre polynomial that we can evaluate for any particular value of n and l. There's also always this exponential piece either the minus z r over one or two or three a naught depending on the value of n for this particular wave function and then comes the angular term so we might have no angular dependence at all when l equals zero. We might have a cosine theta or a sine theta when l is equal to one or when l equals two we might have some second order polynomial and cosine theta that are somewhat familiar to us from when we studied the rigid rotor and lastly we have a term sometimes that looks like e to the i phi or e to the minus i phi e to the two i phi or e to the minus two i phi and that depends on these these values of m so when l is non-zero m can also be non-zero and that results in a complex wave function that has this imaginary term on the end so there's no need to memorize these you can always look them up whenever you need but the point is now that we've written down the general form of the solutions to Schrodinger's equation for the hydrogen atom we could write them down on demand for any n and l and m we wish whenever we want to.