And here what we're using is we're using r theta and, and phi.

The spherical coordinate, coordinate system.

And we mentioned that you need to transfer to this coordinate system.

Because what this enables you to do is it

allows you to, if you like, separate the variables, and

solve the separate equations for the r component, the radial

component, the theta component and the, and the phi component.

And we define these in the, the last presentation.

Because you can break it down into, as we said, a radial part, or times a

function the R, the, the distance of the electron from the central nucleus.

And if you multiply that then by an angular

term, which we define usually as Y theta psi.

Sorry, I meant Y theta phi.

So, we're not, you can solve this differential equation

that's embedded, if you like, in this equation here.

But it's it's quite a difficult solution to do.

And we really, it's, it would be an inappropriate use of our

time to go in to it in detail in, in this course.

And what we're mainly interested in as chemists, is we're interested in these

solutions, or the wave functions and the energies that come out in the solutions.

So, we're going to, we're going to concentrate on them.

Now, first of all like the path in the box, the wave

functions are going to have boundary conditions.

Our boundary conditions are going to be imposed

in the, to obtain the differential equation solutions.

And of course, remember from the part in the box,

it was these boundary conditions that led to the quantization phenomena.

In this case we're talking about a, a three dimensional wave function.

So it's a little bit more, more complex.

But again, the imposition of the boundary conditions will be what will lead to

the quantizations, in other words, the, a ladder of energy levels that will result.