In 1925, W. Heisenberg, Max Born and Pascual Jordan
introduced so-called matrix mechanics.
We assume there is a lot of math and little physics aside from the poorly explained factor of 2^1/2.
This is the first conceptually self-contained and logically coherent formulation of quantum mechanics, but it is still incomplete because it falls short of classical physics problems such as the heat diffusion equation.
However, we believe that the B-matrix string formulation is superior to Heisenberg's because it can solve the heat diffusion equations and quantum mechanical problems in their most general form.
The most important scientific event in the late 1920s was the agreement of the community of quantum physicists on the equivalence of two competing formal explanations of quantum phenomena, namely:
matrix mechanics by Heisenberg, Born and Jordan (HBJ) and wave mechanics by E. Schrödinger.
The equivalence is supported by a rigorous mathematical proof, except that concerning the quantum superposition of the wave function resulting from the Bohr/Copenhagen interpretation where the HBJ fails.
Furthermore, HBJ theory has never addressed the description of macroscopic physical phenomena and is therefore considered incomplete.
It is for these reasons that the general idea was born between mathematicians and physicists that the two theories are irreconcilable.
Unlike HBJ, Schrödinger perceived the field-like continuity of some key microphysical phenomena, such as the interference phenomena of a coherent electron beam in double-slit experiments.
Regardless, in 2020 a new theory emerged (called the Cairo technique) that was found to be able to solve almost all problems in classical physics as well as those in quantum physics.
This means the file is still open and not closed!?
To be continued.
The matrix methods are usually applied
In chemistry with discrete units of atoms
or molecules, or solids in tight binding.
For smooth backgrounds use Schrodinger.
FALL and RISE of Matrix Mechanics
In 1925, W. Heisenberg, Max Born and Pascual Jordan
introduced so-called matrix mechanics (HMJ theory) to study the fine structure of Bohr hydrogen atom. HMJ theory succeeded in finding quantum numbers such as l,m,s in addition to the principal quantum number n.
HNJ proposed a square matrix in general of complex entries that was considered as a matrix formulation of QM and obviously the first MATHEMATICAL formulation of quantum mechanics. conceptually self-contained and logically coherent.
In 1927 Schrodinger equation SE with Bohr/Copenhagen interpretation appeared.
The so-called Copenhagen interpretation of quantum mechanics, which has dominated the field since the 1930s
The equivalence between HMJ theory and SE theory was supported by a rigorous mathematical proof, except that concerning the quantum superposition of the wave function resulting from the Bohr/Copenhagen interpretation where the HBJ fails.
Unlike HBJ, Schrödinger perceived the field-like continuity of some key microphysical phenomena, such as the interference phenomena of a coherent electron beam in double-slit experiments.
At the late 1930th There was a lot of debate about the equivalence of HMJ and Schrodinger equation until the performance of double slit interference experiment which showed clearly that HMJ theory falls short behind SE theory wrt the superposition principle.
HMJ theory contains a lot of math and little physics.
Furthermore, HBJ theory has never addressed the description of macroscopic physical phenomena and is therefore considered incomplete.
This means that HMJ theory is incomplete because it can not address classical physics problems such as the heat diffusion equation.
Additionally, the HMJ and SE equivalence has been debunked and considered a myth.
This is what we call the fall of Matrix Mechanics almost a century ago.
However, In 2020, a new theory of matrix mechanics MM emerged and successfully applied to different areas of classical physics in addition to quantum mechanics.
This is what we call the renaissance or rise of matrix mechanics.
The new matrix mechanics (MM) procedure is called B-matrix chains and is abbreviated as BMM.
In this article, we explain the consecutive steps on how to apply the BMM to different 1D, 2D, 3D situations and how to arrive at the appropriate solutions of the volumetric energy density in the bounded domains.
the transition matrix B or BMM is well defined and it has been successfully applied to different areas of classical physics such as the Poisson and Laplace PDE, the heat diffusion equation, the theory and design of audio rooms, Limited integration in 1D, 2D, 3D. . etc.
Furthermore, the extension of the BMM to find a numerical statistical solution of the time-independent Schrödinger equation in 1D, 2D and 3D was recently described and the numerical results were surprisingly accurate.
Please take a look at,
Fall and rise of matrix mechanics.
Researchgate, January 2024.
IJISRT, January 2024.
We hope that it will provide detailed answers to the interested reader.
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