What do the atomic orbitals of Helium look like?

[sshai45]

Hi.

I am wondering about this. I have been able to find many graphs showing what the atomic orbitals look like for hydrogen, but nothing for more complex atoms, like helium. Why is this? Now I know the Schrödinger equation for helium cannot be solved exactly, but you don't need an exact solution to plot a graph, which will be approximate anyways. Can't you just throw the Schrödinger equation into some kind of numerical differential equations algorithm and plot the results?

ADD: I just remembered that the equation has a psi-function which depends on TWO 3D position parameters, not 1 (1 parameter for each electron), which means it has a 6-dimensional parameter set. So using a grid of 100 points on a side in your numerical algorithm you would need one trillion (10^12) points, which would be several TB of data on a computer. Is this the reason? Even then, couldn't you exploit some kind of symmetry or use a more compact representation like a series expansion or something to cut it down to a more manageable data set?

Also, does the psi-function's dependence on two position parameters mean you cannot really talk of orbitals for each electron after all?

 

[Simon Bridge]

The "orbitals" are usually thought of as the sum of the two single electron states...