None whatsoever.

Normally, we don't comment on answers, but if we find ourselves faced with another Argentina's answer, the situation will be different.

Please note that this answer is empty and provides no information about the question or its answer.

Our Argentinian friend evidently need more time to understand such a 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.

The last century, was marked by the rise of original quantum theory of SE PDE in 1927, but it  is a story doomed to failure and I recommend our Argentinian friend to follow us before it is too late.

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.

TO BE CONTINUED.

The West is losing the battle of quantum mechanics simply because it recognizes only one of the two fundamental theories: 1- Quantum Mechanics (QM) theory based on the original Schrödinger equation and its Bohr/Copenhagen interpretation in 1927.

2- Quantum Mechanics theory based on the squared Schrödinger equation and its interpretation through advanced artificial intelligence in 2020.

Here is one of the most surprising rules that applies strictly to classical diffusion physics, such as the heat equation, and quantum matter diffusion in the squared Schrödinger equation of quantum mechanics.

Thermal diffusion has a maximum limit that cannot be exceeded because it is not permitted by the geometry or shape of the closed volume of a classical system (like a cube of iron or aluminum in classical physics) and by the geometry of the vacuum defined by Dirichlet boundary conditions that encapsulate the quantum system (in quantum mechanics).

Even the intensity of sound in audio rooms has a maximum and minimum decay rate or half time reverberation T1/2.

We will start with the classical heat energy density diffusion equation.

Consider a simple cubic figure of 8 free nodes shown in Fig.1

The statistical B-transition matrix for RO=0.2 (corresponding to α of iron cube) is given by,

0.2 1/6-0.2/3 0 1/6-0.2/3 1/6-0.2/3 0 0 0

1/6-0.2/3 0.2 1/6-0.2/3 0 0 1/6-0.2/3 0 0

0 1/6-0.2/3 0.2 1/6-0.2/3 0 0 1/6-0.2/3 0

1/6-0.2/3 0 1/6-0.2/3 0.2 0 0 0 1/6-0.2/3

1/6-0.2/3 0 0 0.2 1/6-0.2/3 0 1/6-0.2/3

0 1/6-0.2/3 0 0 1/6-0.2/3 0.2 1/6-0.2/3 0

0 0 1/6-0.2/3 0 0 1/6-0.2/3 0.2 1/6-0.2/3

0 0 0 1/6-0.2/3 1/6-0.2/3 0 1/6-0.2/3 0.2

The statistical method of Cairo techniques predicts that,

α=Log(e){[1+RO]/[1-RO]}

Note that RO is ∈ [0,1]

Which means that

α min = 0 and α max = log 2 = 0.673

No diffusion without permission.

Permission comes from the walls and the source term at the speed of light (called entanglement, whose speed is limited to C and not infinity).

It is easy to demonstrate that the general time-dependent solution is given by:

U(x,y,z,t) = [B+B^2+B^3 + . . . +B^N] (b+S) + B^N . IC, . . . . . (1)

Where:

U(x,y,z,t) is the energy density J m^-3

b is the correctly ordered and arranged Dirichlet boundary conditions.

S is the source vector J m^-3 s.

IC is the initial condition vector J m^-3

In the case of a uniform BC [b=constant], it can be shown that the temporal increase in U due to wall emission (first term in Equation 1) is equal to the decrease in U in the IC (second term in Equation 1).

In other words,

[x+x^2+x^3+. . . .+x^N]-[x+x^2+x^3+. . . .+x^N-1] / [x+x^2+x^3+. . . .+x^N] = {(x^N-1) -x^N] / x^N-1]

For all RO (all α) and all IC.

TO BE CONTINUED.

Here are few questions on quantum physics of the Schrödinger equation and classical statistical physics of its square (energy diffusion), to clarify this question and the topic as a whole.

1-Q1-

Briefly explain the Schrödinger wave equation and its square.

A1-

Schrödinger partial differential equation:

i h dΨ/dt)partial=h^2 . Nabla^2 Ψ/2m + V Ψ . . . . (1)

With the Bohr-Copenhagen interpretation introducing entanglement and superposition Ψ.

The Schrödinger partial differential equation is precise but incomplete because it operates in an incomplete D^4 space (3D+t as an external controller). Now imagine solving the Schrödinger partial differential equation for Ψ^2 and not Ψ.

Equation 1 transforms into:

dΨ^2/dt) partial =C1.Nabla^2 Ψ/2m + C2 .V . . . . (2)

With the following statistically proven assumptions,

i-Ψ^2=Ψ . Ψ*

ii-Ψ^2 is exactly equal to the energy density of the quantum particle(s).

iii-Ψ^2 is the probability of finding the quantum particle in the 4D unit volume element x-t "dx dy dz dt"

iv- The actual time t is completely lost and replaced by the dimensionless integer N dt. In this 4D unit x-t space, the dimensionless time N is integrated into the 3D Cartesian space.

N is the number of iterations or repetitions and dt is the time jump.

Equation 2 is derived from and solved by the advanced artificial intelligence of modern transition matrix statistics.

Equation 2 is solved via matrix mechanics and does not require any PDE or FDM techniques to be solved.

Surprisingly, equation 2 is more informative than equation 1.

Q2

Is the quantum wavefunction Ψ a scalar, a vector, or neither?

A2

It is very likely that Ψ is none of these.

The quantum function Ψ^2 is an nxn square matrix (second-order tensor).

The question arises: is the answer to this question "shut up and calculate"?

Q3-

Is the Schrödinger equation an eigenvalue problem?

Is the heat diffusion equation an eigenvalue problem?

A3

The answer is yes in both cases.

Solving the heat diffusion equation using advanced AI for matrix chains B is an eigenvalue problem.

The most important thing is the preliminary selection of the principal diagonal elements RO (entries) of the statistical transition matrix B.

The solution is expressed by the transfer function of the heat diffusion equation D(N):

U(x,y,z,t)=D(N).[b+S] +B^N IC

IC is the vector of initial conditions (U(x,y,z,0))

The eigenvalue of the solution implies:

the exponent of the solution:

k*= log [(1 + RO) / (1-RO)]

Note that [(1 + RO) / (1-RO)] is equal to the eigenvalue 1 for B and [(1 + RO) / (1-RO)]^2 to the eigenvalue 2 for B^2, etc.

with a maximum of log 2 and a minimum of zero. [RO] is the diagonal vector of matrix B.

Vector RO = ( RO11 , RO22, RO33 , . . . ,RO n n)

The classical approach to the Schrödinger equation is an eigenvalue equation:

By definition, an operator acting on a function produces another function. However, a special case arises when the generated function is proportional to the original function.

A^ψ∝ψ . . . (1)

[This is a special case]

This case can be expressed as an equality by introducing a proportionality constant k.

A^ψ = k ψ . . . . . (2) [This solution applies to the special case of PDEs]

Not all functions solve an equation like those in equations 1 and 2.

ψ = (φ1+φ2)/√2

TO BE CONTINUED.

The statistical theory of Cairo techniques allows us to explain this complex situation in more detail:

The time-dependent diffusion equation (like the Laplacian operator equation) represents or models the natural binary collision relaxation process in a closed-surface control volume subject to Dirichlet boundary conditions.

1- In both time-dependent and time-independent processes, the information waves are always contained within the same control volume.

2- This means that the diffusion process is associated with and controlled by the information waves filling the control volume, both in macroscopic classical physics, such as the macroscopic heat diffusion equation, and in microscopic subatomic quantum physics.

Information waves are the driving force: no diffusion without permission.

Note that information waves are transmitted at the speed of light C.

3- This means that the Schrödinger partial differential equation is not a pure wave equation, but a partially diffusion and partially wave equation. 4- When we attempt to extract information from a quantum system through measurement, the information wave diminishes and the system transforms into a pure scattering system, a system of colliding particles.

This is sometimes called quantum wave collapse.

To be continued.

Earthquake seismology (the propagation, reflection, and refraction of Earth's seismic waves) is the best tool for understanding the Earth's interior.

It also allows us to understand the Earth's interior.

It also explains the techniques of Cairo's statistical theory, combined with the theory of information propagation (the propagation, reflection, and refraction of information waves).

During an earthquake, the released energy takes the form of elastic waves transmitted by diffusion through the Earth.

However, this diffusion (propagating at a speed of a few kilometers per minute) is guided or controlled by the much faster information sphere, which propagates at the speed of light C.

Seismic wave propagation is ground movement, including compressional and shear waves, radially from the source of seismic energy (source center S) to the surrounding rock and soil. Seismic wave fields propagate through the Earth in two ways: body waves and surface waves. Body waves propagate within the Earth (body) and illuminate deep geological targets. It is noteworthy that seismic wave propagation follows the shortest path theory, with refractions predetermined by the information sphere's exploration command, similar to the refraction of light and electromagnetic waves between two media.

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.