I have written a mathematica notebook to plot hydrogen orbitals. Then my professor wanted to plot a helium orbitals. Well, really it would be like hyrodgen,but with distorted from electron-electron interaction. Well, the differential equations are partically impossible to solve. So, we using the Variational Principle to find a trial function. They way we are doing it(our trial function is pretty much a polynomial times an expotential so we break the wave function according to the varational parameters[see the notebook]) Therefore,the answer is in the form of quadratic form. So, we can put it in the form of a matrix.
The elements in the matrix are extermly small(see the notebook) so the I feel the Decompositions and Martix operations yeiling serious numerical errors...
But could be something wrong witht he traily function.
Note: evaulation will be lengthy.
Attachment: OrbitalsDrawn.nb, URL: ,