This post has reference to my earlier post of 30th March 2019, here [^]. Being busy mainly with learning Data Science, I didn’t subsequently find the time to systematically study the papers and the book which were suggested by the IIT Bombay professors back in March-end.
However, in the meanwhile, thinking about the whole issue independently (and on a part-time basis), I have come to work through a detailed scheme for calculating the wavefunctions for the case of a 1D helium atom.
In particular, the abstract case I have worked through is the following:
A single helium atom placed in a 1D domain of a finite length, and with either reflecting boundary conditions (i.e. infinite potential walls) at the two ends (i.e. a 1D box), or possibly also with periodic boundary conditions imposed at the two ends (i.e. an infinite 1D lattice of 1D helium atoms). The problem is to find the energy eigenstates for the system wavefunction, assuming that the electrons do interact with each other.
The electrons are spinless. However, note, I have now addressed the case of the interacting electrons too.
I have not performed the actual simulations, though they can be done “any time.”
Yet, before proceeding to write the code, I would like to show the scheme itself to some computational quantum chemist/physicist, and have a bit of a to-and-fro regarding how they usually handle it in the mainstream QM/QChem, and about the commonality and differences (even the very basic reasonableness or otherwise) of my proposed scheme.
I can even go further and say that I have now got stuck at this point.
I will also continue to remain stuck at this same point unless one of the following two things happens: (i) a quantum chemist having a good knowledge of the computer simulation methods, volunteers to review my scheme and offer suggestions, or (ii) I myself study and digest a couple of text-books (of 500+ pages) and a few relevant papers (including those suggested by the IIT Bombay professors).
The second alternative is not feasible right now, simply because I don’t have enough time at hand. I am now busy with learning data science, and must continue to do so, so that I can land a job ASAP. (It’s been more than a year that I have been out of a job.)
So, if you are knowledgeable about this topic (the abstract case I am dealing with above, viz., that of 1D helium atom with spinless but interacting electrons), and also want to help me, then I request you to please see if you can volunteer just a bit of your time.
If no one comes to help me, it could take a much longer period of time for me to work through it all purely on my own—anywhere from 6–8 months to a year, or as is easily possible, even much more time—may be a couple of years or so, too. … Remember, I will also be working in a very highly competitive area of data science too, during all this time.
On the other hand, to someone who has enough knowledge of this matter, it wouldn’t be very strenuous at all. He only has to review the scheme and offer comments, and generally remain available for help, that’s all.
(It would be quite like someone approaching me for some informal guidance on FEM simulation of some engineering case. Even if I might not have modeled some particular case myself in the past, say a case of some fluid-structure interaction, I still know that I could always act as a sounding board and offer some general help to such a guy. I also know that doing isn’t going to be very taxing on me, that it’s not going to take too much of my own time. The situation here is quite similar. The quantum chemist/physicist doesn’t have to exert himself too much. I am confident of this part.)
So, there. See if you can help me out yourself, or suggest someone suitable to me. Thanks in advance.
A song I like:
(Marathi) “vaaTa sampataa sampenaa…”
Lyrics: Devakinandan Saaraswat
Music: Dattaa Daavajekar
Singer: Jayawant Kulkarni