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Schrodinger equation just a misrepresentation of wave equation of electromagnetic wave equation of light in the electric dipoles of aether and it has nothing to do with Big Bang Theory.

However after discovery of aether and proving Einstein's theory of relativity as baseless there is a standing open challenge to theory of relativity, Space-time Concept and Big Bang Theory since 2012 as all the attempts to disprove it failed miserably. See the open challenge in my profile on ResearchGate.

Ismail Abbas M. Abbas ,

The solution to the Schrödinger equation generally does not allow for singularities in the same way that general relativity does. The Schrödinger equation is a linear partial differential equation governing wavefunctions, which describe quantum systems. These wavefunctions must remain finite and normalizable (i.e., their total probability integrates to one), which rules out the presence of singularities where the probability density would become infinite or undefined.

In contrast, general relativity permits singularities—points where physical quantities such as density and curvature diverge—because it is a classical, nonlinear theory. The Big Bang and black hole formation are both predicted to involve such singularities, where known physics breaks down. Since the Schrödinger equation does not accommodate such infinite-density points, this suggests that a purely quantum mechanical description of the universe (or black holes) would need a deeper framework beyond standard quantum mechanics.

This discrepancy is one of the major motivations for quantum gravity theories. In approaches like loop quantum gravity or string theory, it is often suggested that quantum effects could remove singularities, replacing them with a new physical regime where space and time remain well-defined. Some proposals even suggest that the Big Bang singularity is replaced by a quantum bounce, where a prior collapsing universe transitions into expansion.

Thus, while the Schrödinger equation alone does not allow for singularities, this does not necessarily mean that singularities are physically real. It instead suggests that quantum mechanics, as currently formulated, is incomplete when dealing with extreme gravitational collapse or the origin of the universe, pointing toward the need for a quantum theory of gravity.

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)/√ Note that equation 1 does not allow for singularity while equation 2 does.

Note that Equation 1 Does not allow a singularity whereas equation 2 does.

TO BE CONTINUED.