The short answer is yes, it is absolutely true.
We first affirm that the matrix mechanics of W. Heisenberg, Max Born and P. Gordon (H-B-G) was born dead and destroyed by the Schrödinger equation in three years.
This is not surprising since the HBG matrix is designed to resolve energy levels in the hydrogen atom and is therefore only a subset of SE PDE.
On the other hand, modern statistical mechanics (B matrix chains and Cairo techniques in 2020) has established itself as a giant capable of solving almost all physics and mathematics problems.
Here we can say that it is a unified field theory and Schrödinger's PDE is one of its subsets and not vice versa.
We predict that future scientific research over the next ten years will increasingly focus on the area of modern matrix mechanics, at the cost of eliminating the Schrödinger equation.
The short answer is yes, it is absolutely true.
It is worth mentioning that the proposed matrix mechanics called matrix B transition chains is completely different from the matrix mechanics of W. Heisenberg, Max Born and P. Gordon (H-B-G).
Furthermore, we believe that B-matrix transition chains have proven themselves as a unified field theory, capable of solving almost all problems in physics and mathematics.
On the other hand, H-B-G was born dead and destroyed by the Schrödinger equation within three years.
This is not surprising since the HBG matrix is designed to resolve energy levels in the hydrogen atom and is therefore only a subset of SE PDE.
Once again, we emphasize here that modern statistical mechanics (B-matrix chains and Cairo techniques in 2020) has emerged as a giant capable of solving almost all physics (microscopic quantum situations such as the partial differential equation of Schrödinger and macroscopic classical situations such as the heat diffusion equation in addition to pure mathematical problems such as statistical integration and differentiation) as well as mathematical problems of partial differential equations.
Here we can say that it is indeed a unified field theory and that Schrödinger's PDE is a subset of it and not the other way around.
We predict that future scientific research over the next ten years will increasingly focus on the area of modern matrix mechanics, at the cost of minimizing the Schrödinger equation.
This is just a brief answer which aims on the one hand to clarify the question and its answer and on the other hand to thank our fellow contributors for their helpful answers.
It is true that extraordinary allegations require extraordinary evidence.
Unlike the Schrödinger equation and its derivatives, B matrix chains and Cairo statistical techniques are capable of numerically solving almost all energy fields [1,2,3,4,5] of quantum physics and from classical physics like the Poisson and Laplace PDE, heat diffusion equation, sound intensity in audio rooms in addition to pure mathematical problems such as differentiation and integration.
We assume that this makes it a unified field theory.
The references:
1-An efficient reformulation of Schrödinger's partial differential equation
Full text available
May 2024, Researchgate, IJISRT journal.
2-Is it time to reformulate the Poisson and Laplace partial differential equations?
Article
Full text available
June 2023, Researchgate, IJISRT journal.
3-A statistical numerical solution for the time-dependent 3D heat diffusion problem without the need for the PD heat equation or its FDM techniques.
Full text available
July 2021, Researchgate, IJISRT journal.
4-Theory and design of audio rooms -A statistical view, Full text available
July 2023, Researchgate, IJISRT journal.
4-Effective unconventional approach to statistical differentiation and statistical integration
Full text available
November 2022, Researchgate, IJISRT journal.
It is easy to show that unified field theory belongs to the square of the Schrödinger wave equation rather than to the classical Schrödinger wave equation itself.
You first transform the Schrödinger PDE describing the wave function Ψ into another describing its square Ψ^2=Ψ. Ψ*. Strikingly, the modified Schrödinger PDE describing Ψ^2, when supplemented by the natural laws of vacuum dynamics, is more complete than the classical Schrödinger PDE itself.
The reformulated Schrödinger partial differential equation lives and operates in the 4D unit space and therefore belongs to the chains of the B matrix which is a product of the statistical method called Cairo techniques.
You can take a particular approach to show that unified field theory belongs to the square of the Schrödinger wave equation rather than the classical Schrödinger wave equation itself.
This particular approach focuses on applying B-matrix chain techniques to answer three fundamental questions that continually challenge the classic Schrödinger equation:
A-Can we replace Schrödinger's partial differential equation with a kind of statistical matrix mechanics capable of describing the formation and explosion of the Big Bang?
B-Can we deduce an expression for the reverberation time in audio rooms?
C-Is it possible to calculate a finite numerical integration via matrix mechanics?
Mathematicians and theoretical physicists with the greatest skills in the classical Schrödinger equation cannot answer these particular questions even in their dreams.
Finally, we present a correct and exact answer to the three questions A, B and C [1] proving that the unification of field theory is the square of the Schrödinger wave equation sublimated by the rules of vacuum dynamics and that the dynamics of nature is nothing but matrix mechanics.
1-Is unified field theory Schrödinger's wave equation or its square? A unitary spatio-temporal vision, ResearchGate, IJISRT journal, July 2024.