Many physicists and mathematicians assume that mother nature has two distinct languages, one for macroscopic objects in classical physics and the second for microscopic subatomic objects which is Schrödinger's PDE and its derivatives.

Moreover, the old iron guards of SE believe that these two languages ​​​​reduce to a single one which is the solution of SE, Many physicists and mathematicians assume that mother nature has two distinct languages, one for massuming that eventually it can deal with macroscopic objects (Via SE has no scales and principle of Correspondence).

The opposite is true:

The Schrödinger equation is only a subset of modern probability classical mechanics.

SE itself is a probability conservation equation!

We assume that nature has only one language to speak to itself, namely the physical statistical chains of the B matrix capable of solving the classical heat diffusion equation and the quantum Schrödinger PDE in a configuration space 3D.

It is striking that the closed, empty configuration bounded in 1D, 2D and 3D has its own probability and statistics, even without any energy density field inside.

A striking example of the above statement appears in limited mathematical integrations:

I= ∫ y dx from x=a to x=b, . . . . (1),

I=∫∫ W(x,y) dx dy from x=a to x=b and y=b to y=c. . . . . (2)

..etc..

Equations 1,2 can be calculated numerically and precisely via the transition chains of the matrix B[1] by applying the so-called statistical weights,

I{1D,7 nodes}=6 h /77(6*Y1 +11* Y2 + 14* Y3+15* Y4 +14* Y5 + 11*Y6 + 6*Y7). . . . (1*)

I{2.9 nodes}= 9 h^2 /29.5

2.75 3.5 2.75

3.5 4.5 3.5

2.75 3.5 2.75

(Y11,Y12,Y13,Y21,Y22,Y23,Y31,Y32,Y3) .. . . (2*)

NOW, believe it or not, equations 1*,2* are exactly the numerical statistical solution for ψ(r)^2 in the time-independent Schrödinger PDE.

[1]Effective unconventional approach to statistical differentiation and statistical integration, Researchgate, IJISRT [1]Effective unconventional approach to statistical differentiation and statistical integrjournal, November 2022.

[2]Cairo Techniques Solution of Schrödinger's Partial Differential Equation -Time Dependence, Researchgate, IJISRT, March 2024.