Born from the imagination of Planck, Schrödinger, Bohr, and others, this theory is inherently incomplete, unreliable, and doomed to disappear sooner or later.
Einstein stated that Schrödinger's PDE is incomplete perhaps because it operates in R^4 space (3D with real time as the external controller) and not in 4D unitary x-t space.
Quantum mechanisms live and operate in infinite free space (nearly zero gas molecules).
1-First, Schrödinger's PDE should be replaced by its square in 4D unitary x-t space within a control volume bounded by Dirichlet boundary conditions and a potential energy V correctly defined by:
V = C1. V1 + C2. V2. . . (1)
Where V1 is the externally applied voltage and V2 is the spontaneous or self-applied voltage.
V2(x,y,z,t) = Cons. U(x,y,z,t) . . . (2)
Where U is the quantum energy density. Clearly, C1 + C2 = 1.
Therefore, the Schrödinger partial differential equation (PDE) is partly a diffusion equation and partly a wave equation.
It should be noted that Equations 1 and 2 are not suggestions, but rather equations of certainty.
2-Once the vacuum energy/temperature is defined, quantum dark energy and dark matter can be explained:
Vacuum dark matter/energy, i.e., particle-antiparticle pairs (equations 1 and 2) generated and mutually annihilated in deep space, is considered the main contributor to dark energy.
Mass can be created in antiparticle pairs, but not charge.
Note that:
i- The B transition matrix is very different from the useless QM density matrix, which is neither statistical nor complete.
ii- The Schrödinger PDE solution does not account for the singularities essential to the formation and explosion of the Big Bang, nor for the collapse of giant stars into tiny black holes, unlike the string B matrix solution.
What else?
We all know that the Schrödinger equation is very effective in explaining the observed experimental phenomenon of quantum particle tunneling.
Let's analyze a misleading error in a Wikipedia-Google search.
"Tunneling is a consequence of the wave nature of matter. The quantum wavefunction describes the state of a particle or other physical system, and wave equations, such as the Schrödinger equation, describe their behavior.
This is called quantum tunneling!"
But this is only an illusion, because the artificial intelligence of Cairo's techniques allows us to deduce the formula for quantum tunneling from the square of the Schrödinger equation, using classical statistics.
In reality, the artificial intelligence of Cairo's techniques allows for the superposition of total energy in the classical sense. Therefore, quantum tunneling can be rigorously described from the square of the Schrödinger equation, using the statistics of Cairo techniques.
Step 1
Find the allowed stationary solution to the proposed quadratic equation for a quantum particle in a one-dimensional infinite potential well using the statistical chains of matrix B, i.e., 1/n^2, 1, 1/4, 1/9, 1/16, etc. (as shown in Figure 1).
Step 2
The above values correspond to the eigenenergies: 1, 4, 9, 16, etc.
Step 3
Apply the superposition principle, i.e., E = (1, 4, 9, 16, etc.)
with probabilities P1, P2, P3, etc.
Step 4
If the quantum system (or particle) has a total energy Etotal, then:
Etotal = P1 * E1 + P2 * E2 + P3 * E3 +...PnEn
The tunneling problem is reduced to solving the algebraic equation:
X is a function of the total energy such that:
for x .LT.1
X + X^2 + X^3 + . . = Etotal
Step 5
In exponential form, for x .LT. 1:
e^x + e^2x + e^3x . . = Etotal
OR,
1/(1-e^x)=Etotal
Obvious example: for x = 2/3, then Etotal = 3 units.
Step 6
Transmission or quantum tunneling part:
Transmission or quantum tunneling part:
e^ (- Alpha b).Etotal.e^-1/(1-x).GE.Uo (tunnel edge)
Fig. 2
Where l is the barrier width and Alpha is the exponential decay coefficient.
The tunneling ratio Etransmitted/Eincident is called Transmission T=e^-Alpha . l e^- (Etotal/Uo)
Where x = Etotal/Uo . . . (1)
Formula 1 is equivalent to that derived from solving the Schrödinger partial differential equation.
It should be noted that the artificial intelligence approach of the Cairo techniques is fundamentally different from that used to solve the Schrödinger PDE.
To be continued.
1-A statistical numerical solution for the time- independent Schrödinger equation, ResearchGate, IJISRT journal, November 2023.
Normally, we don't comment on answers, but if we find ourselves faced with Argentina's answer, the situation will be different.
Please note that this answer provides no information about the question or its answer.
Our distinguished Argentinian friend may need more time to understand the topic.
In fact, there are currently two distinct theories of quantum mechanics:
i- The original Schrödinger PDE in 3D +t space, which is incomplete.
ii- The modern square of Schrödinger PDE theory in 4D unitary x-t space, which is complete.
From these two distinct theories, several options are available for the specifications of quantum mechanics. However, the second theory has proven superior, as explained below in published articles. It is important to note that:
i- Schrödinger's original proposal (1925-1929) exists and operates in R^4 space (3D with real time as an external control), which is an incomplete and inadequate space.
ii- The new theory of quantum mechanics, based on Schrödinger's original squared PDE, operates in the 4D spatial unit x-t, which is complete space.
It is worth noting that the second approach, thanks to advanced artificial intelligence, is more efficient and avoids all the problems of quantum mechanics.
Below we present some published articles to further explore the topic:
1- A statistical numerical solution for the time-independent Schrödinger equation.
Full text available
November 2023
2- Numerical statistical solution of the time-independent Schrödinger equation - Part II
December 2023
3- 3D numerical statistical solution of the time-independent Schrödinger equation
Article
Full text available
December 2023
4- Rise and fall of matrix mechanics
January 2024
5- Spontaneous statistical solution of the Schrödinger partial differential equation
Article
Full text available
Feb. 2024
Cairo Techniques
6- Solution of the Schrödinger partial differential equation - Time dependence
7- An Efficient Replacement for the Schrödinger Partial Differential Equation
April 2024, International Journal of Innovative Science and Technology
DOI: 10.38124/ijisrt/IJISRT24APR1768
8- An Efficient Reformulation of the Schrödinger Partial Differential Equation
May 2024
9- Quantum Hum, Vacuum Dynamics, and the Big Bang
June 2024, International Journal of Innovative Science and Technology
DOI: 10.38124/ijisrt/IJISRT24JUN1700
10- BOOK: Foundations of Artificial Intelligence,
March 2025
etc.
The last century, marked by the rise of original artificial intelligence, is a story doomed to failure and I recommend our Argentinian friend to join us before it is too late.
This is a brief reply, essentially aimed at correcting a serious typo in the previous answer, which should read as follows:
The last century, marked by the advent of the original Schrödinger equation, is doomed history, and I recommend our Argentinian friend to join us before it's too late.
We also add that one of the most important problems where the second theory of QM surpasses the first is that of the vacuum in infinite free space where QM itself lives and operates.
It is in this external dark space that we can define dark energy and dark matter, as well as the vacuum temperature.
To be completed.
Now we all know that there are two distinct theories of quantum mechanics: i-The quantum mechanics theory based on the original equation of Schrodinger and supplimented with the principle of superposition with Bohr interpretation in 1927. ii-The quantum mechanics theoy based on the square of original Schrodinger equation supplimented with the artificial intelligence of the statistical theory of Cairo techniques prosedposed in 2020 We recall once again that this second theory of quantum mechancs deals with and even improves all quantum properties of the original SE such as entanglement, superposition and quantized energy solutions. However, the main objective of this Q/A is to examine the possibilty of combining the theory of quantum mechancs with the theory of general relativity (gravitation) to arrive at a better understanding of the darkenergy and dark matter in the outer deep space. Answer of this qustion that prove that electromagnetic field energy can be transformed into gravitational field energy and vice versa via the second theory of quantum mechanics offers a positive answer.
SIMPLE CHALLENGE
The simple challenge to our distinguished contributors and readers is the statistical transition matrix B for a closed control volume of surface A subject to Dirichlet boundary conditions,
U(x,y,z,t+dt)=B. U(x,y,z,t) . . . (1)
Equation 1 is not only universal, but it also describes and solves all time-dependent phenomena in the entire universe (partial differential equations of classical physics in its most general form, quantum physics, statistical distributions, integration and differentiation, etc.).
The challenge is as follows:
Name a single physical phenomenon from the four above that does not belong to Equation 1.
Thank you.
Its one of the most succsesfull theories in terms of
wide ranging predictibily, spectroscopy, chemistry or nuclear science.
As to new theory there is only modern QM. Opposed to the old up to 1925.
You can use differential operators or matrices.
I would not claim much else
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