A preliminary document on my fresh new approach to QM

For the sake of ... no other word but ``idiots'', esp. the American borns / intellectual goons:

https://ajitjadhav.wordpress.com/2017/12/12/yes-i-know-it-part-2/

https://ajitjadhav.wordpress.com/2017/12/11/yes-i-know-it/

Often the issue also applies to many (but not all (but excepting for only a very small insignificant minority of)) the past Indian immigrants to the USA.

Sincerely,

--Ajit

Please see at my personal blog, here [^].

Best,

--Ajit

Hi all:

只是一个更新。也许太详细,但想ss it's good to leave a record of where things stand, as of today...

1. Theoretical development for the spinless massive particles is over:

Ithinkthat, by last night (India time), I had satisfactorily resolvedallmajor theoretical issues pertaining to understanding a quantum system of two spinless electrons, using my new approach to QM. This included the tricky issues such as: (1) quantitative predictions for the motions of particles, and (2) the issue of how the system wavefunction, defined as it is over the $3N$-dimensional configuration space, relates to the physical fields I have posited as existing only in the $3D$ physical space.

2. There are significant changes from the above document:

There are considerable changes and revisions to be made to the theoretical positions/explanations mentioned in the above-mentioned PDF document (attached to the main post here).

Indeed, rather than revising the above document, I now plan to write, completely fresh, a set oftwo new documents, and to upload their initial versions here at iMechanica. The two documents will be posted in separate posts (and not right in this thread, though I will provide a link from here).

The first of the two planned documentswill address the spinless, massive elementary particles (electrons &/or protons). The second document will then add the considerations arising due to the quantum spin, and further modify the description as necessary. As of today, I donotplan to address detailed theory/computational modelling for photons at all.

Although there are a lot of changes necessitating a completely fresh write-up for my new approach, many of the points mentioned in the above documents are found to hold well. Some of these have been of crucial importance too.

3. Time estimates:

The estimate for completing the new planned document on the spinless particles, together with its accompanying Python code, is about two months, i.e., by February 2021-end. As of today, I am not clear when the second (i.e. spin-related document) may get completed, though I do already have a lot of material ready for it too.

As to the spinless particles:

I've already implemented the hydrogen atom in a 3D box, but the helium atom will be the first important test for my new approach. I can only hope that the results turn out to be satisfactory. One of the important reasons I say "hope" is because there are certain tricky issues, discussed below.

4. A problem area:

Although thetheoryof the new approach is now quite fully clear (at least for the spinless particles), I've noticed that a lot of subtle issues come up incomputationally modeling and solvingthe eigenvalue equations.

特征值计算,我使用SciPy桅杆e-array functions, and sometimes also verify these results using LinAlg's dense-array functions (which is only feasible for very small systems).

While modelling the hydrogen atom in a3Dbox using these libraries, I have observed that the reported eigenvalues are unduly sensitive to the mesh size.

One important reason may be that while the Coulombic field is theoretically singular, the finite difference approximation can work only with a finite depth for the potential energy well.

The relative coarseness of the mesh also should be an issue, simply because there must be discontinuities even in the first-order spatial derivatives in FDM, and if the discrete jumps in the gradients are too high, the eigenvalue solver wouldn't be able to respond very well. For instance, I have observed that with even small changes in the mesh count, e.g., just from 50 nodes per side of the simulation cube to 52 nodes, the ground-state eigenvalue changes a great deal: from about -0.48 hartree to -0.21 hartree or so, a difference of more than 200 %! For comparison, the analytical solution is available; it's -0.5 hartree, exactly. The physical side of the box in all cases was 1 nm (i.e. almost 18.7+ Bohr radii).

So, the FDM may not be the idea method to use for this problem, in this regime of mesh refinement. On the other hand, my laptop doesn't have capacity to handle adequately refined mesh (say 500, 1000, or 2000 nodes per side).

5. My planned course of action:

My current plan is to pursue the simplest possible numerical techniques, so that I can better focus attention onshowing how the new approach can at all be used。的objective isto make the theoretical structure of the new approach clear, even if the numerical results aren't all that satisfactory.

This means continuing to use FDM and the readymade Python libraries, at least until the first of the new planned documents is completed.

For the same reason, I am postponing any studies/implementation of the mainstream QM techniques, esp. the variational method.

6. Other factors:

Much of the uncertainty concerning this entire project arises from the aforementioned kind of computational aspects alone.

Any other major issues, if they become "show-stoppers", will be noted via a further comment at this thread. (Such things can also include RSI (repetitive injury syndrome) which has affected me for the last 3--4 months. It has reduced a lot by now, but if it aggravates once again, there will be further delays.)

7. I am taking this up on priority:

I am now getting going withcomputational implementation for modelling the helium (He) atom in 1D and 3D boxes, using my new approach, starting right today。

(However, potential employers need not wait for its completion. I would be able to implement everything on a part-time basis, say purely on week-ends, and still be able to keep the schedule mentioned in this update.)

8. Request to you:

If you know of any 1D or 3D implementations (esp. in Python or C/C++) for the He atom, then kindly alert me to them.I could use perhaps use them for benchmarking purposes.

Otherwise, kindly hold your comments, questions etc., until the initial version of the first document is uploaded. Thanks in advance. (You won't have to wait for any more than twomonthsnow! Contrast: The above document was uploaded almost twoyearsago.)

Wish you all a very happy, productive, and prosperous new year!

Best,
--Ajit

1. Check out this one status at:

https://twitter.com/AjitRJadhav/status/1349352312062570497

2. No, I'm not currently in a mood to update this one, updated last year, on 25 May 2020:

https://jadhavresearch.wordpress.com/

I am still jobless. You should LOVE Indian IT industry. No, You MUST! The way you ALWAYS did!

3. Check the MONEY you made last year.

4. Bye for now.

Best,

--Ajit