No-it would be useful to actually (a) read their paper (and it's Pascual Jordan, not Pasquale Gordon) and (b) study quantum mechanics.

This is Heisenberg's paper: https://wucj.lab.westlake.edu.cn/Others/Heisenberg_Quantum_Mechanics.pdf

This is the paper Born wrote with Jordan: http://www.neo-classical-physics.info/uploads/3/4/3/6/34363841/born_and_jordan_-_qm_1.pdf

after that;

and this is the paper all three wrote together: http://fisica.ciens.ucv.ve/~svincenz/SQM333.pdf

With search engines there's really no excuse.

Of course to learn quantum mechanics, these aren't, necessarily, the most suitable papers.

These lectures: https://www.damtp.cam.ac.uk/user/tong/quantum.html might be more suitable.

This is only a brief answer, on the one hand to shed more light on the question and its answer and on the other hand to thank our sincere French colleague for his answer which touched neither on the question nor on his answer.

He recommends reading the article by

idols W. Heisenberg, Max Born and Pasquale Gordon which is incomplete.

I doubt he understood the question well because it is a bit difficult and multi-directional.

I try to make things simpler below,

1-How about solving the Laplace and Poisson PDE via B-string matrix mechanics?

2-How about solving the heat diffusion equation via B-chain matrix mechanics?

3-How about solving the 3D electric potential distribution via B-string matrix mechanics?

4-How about the 1D, 2D, 3D energy distribution of a quantum particle via B-chain matrix mechanics?

5-How about solving single, double and triple bounded integrals via B matrix mechanics?

. . .etc.

All items 1-5 and above have only one meaning:

the matrix mechanics of the idols W. Heisenberg, Max Born and Pasquale Gordon are incomplete.

Finally, a little advice to our French friend:

You cannot turn off the sun and the B-matrix string theory from the Cairo technique will sooner or later dominate almost all areas of science.

It's better to join before it's too late.

It is possible to recover classical mechanics from quantum mechanics, just the matrix mechanics of Heisenberg isn't the easiest way to do so, nor even the approach by Schrödinger; it turns out that the path integral formalism of Feynman is the easiest way to understand how the classical limit emerges.

(Though there are exceptions.) But `` easier'' is, just, a question of personal taste.

What is non-trivial-and not a question of personal taste-is the proof that all three descriptions of quantum phenomena are mathematically equivalent. That proof is in many textbooks on quantum mechanics or quantum field theory.

The questions asked have well-known answers:

The Poisson equation is nothing more or less than the classical equation of motion of a Gaussian field, with an external source and the Laplace equation is the classical equation of motion of the same field, in the absence of an external source. Both equations, indeed, can provide as solution the-classical-potential distribution (if the Gaussian field is identified with the scalar potential), so it doesn't make sense pretending they don't. If that fact isn't known, it should be learned.

The heat diffusion equation, in turn, describes a particular-classical-conservation law, that can be straightforwardly deduced using the path integral. So its solution, in fact, can be identified with the source of an appropriate field.

However focusing on these issues misses the point that the object of matrix mechanics/Schrödinger equation/path integral is to take into account fluctuations, to go beyond the solutions of the equations of motion.

The statistical properties of the eigenvalue distribution of a matrix can be and have been described using matrix mechanics (this was done by Wigner and Dyson in the 1950s and has been pursued since). They can, also, be obtained from the Schrödinger equation and the path integral-nothing new here, either.

Matrix mechanics doesn't have as object the calculation of arbitrary integrals, its focus is on other topics.

It doesn't make sense to pick at random papers by ``famous'' people and then complain that these papers don't contain the solution to problems one is interested in and deduce that they don't deserve their fame, because their work doesn't provide the solution to the particular problem one is interested in. Their paper wasn't written with the needs of someone in the future in mind.

And problems are solved by calculation, not by incantation. It's easy to make claims, harder to actually back them up with evidence. If you know how to solve a problem, one method suffices. If you have it, I don't understand what you're going on about. There are many methods for solving the same problems, which one is chosen doesn't matter, only obtaining the solution matters. The usefulness of any method depends on the ease with which one can use it to obtain the solution of the problem of interest. But discussing which method is used for solving any problem is pointless, it's a question of taste.

So, instead of complaining that some method isn't useful for solving some problem and chanting the name of another method, why not showing the publications that explain how the new method actually solves the problems it purports to be able to solve and what are its advantages with respect other methods? Nobody's ever claimed that the methods for solving problems are unique.

Normally I don't comment on misleading answers, but when it comes from our sincere French colleague, it would be different.

I have a lot of sympathy and admiration for him because each time his answer comes, it shows a leap in his understanding of the difficult subject of matrix mechanics.

1- What about resolving sound field energy density distribution in audio rooms via B-matrix mechanics?

Can it be solved via the Heisenberg matrix or even the Schrödinger equation or any other way[1]?

2-We agree with some of R. Fenman's achievements but he makes his own serious errors when he falsely claims to understand the special theory of relativity[2].

Finally, I recommend to our French friend to judge for himself and not dance to the Russian drums of his idols.

1-Theory and Design of audio rooms -A Statistical View, IJISRT review, July 2023.

2-A rigorous reformulation of Einstein derivation of the special theory of relativity, IJISRT review, Feb 2022.