I wonder how the electrons in a heavy atom or in a complex molecule behave.
Because all of the electrons in a complex system are suffering from a same common nuclear potential field.
Of course, the stete and behavior of the nucleii are by themselves difficult problem to solve.
Since all of the electron are equal, I don't understand why the ordinary textbooks emphasize that an electron is in a state of the systemtically classified states like K shell, L shell SP-hybrid state etc. Or am I wrong at some important point?
As a basic research, I am working to make programs of Schroedinger eigenvalue problem and Schroedinger time dependent equation.
By the limit of the speed and memory capacity of the personal computer now abailable, I have to satisfy doing 2D-1B problem or 1D-2B problem.
For the above mentioned subjects to be solved by personal computer, it looks like to take future time beyond my life time.
At present, only one thing, I would like to comment.
It is this. As long as the interaction potential functions are same for all time, time developmental simulation show that the system necessarily returns to its initial state. So that, if we could make a collision program for realistic two 3 dimensional hydrogen atoms each of which are constituted from electron and proton, the simulation cannot yield synthesized hydrogen molecule whatever the initial 12 variables function may be.
Therefor, for me, we need something other to make chemical reaction occur.
However, I have ever succeeded in a transition simulation of simple system.
There, two things were absolutely necessary. One thing is of course to obey the energy conservation law, that is, the energy that one system gaines must eqaul to the energy that the another system lose. The second thing was an artificial ephemeral working coupling term. Although I do not know yet the the true character of the ephemeral coupling term, but if it is adjusted exactly,it functions to cause the very quantum mechanical transition.
Thus I cannot but speculate third thing other than the two chemical reagents which are the main players involved in a general chemical reaction.
As a last word, for any chemical problem, there are involved many many electrons and nuclei. How should we devise a way to solve the many electron-many nuclei Shroedinger time-dependent equation to simulate and understand a real chemical reaction?