The answer to both questions is yes, but Schrödinger's original iron guards, made from the remainder of physicists and mathematicians, remain safe and effective.
Schrödinger's iron guards in matrix mechanics from PDEs (born between 1925 and 1927) have been brainwashed but are still much alive and operating contrary to facts and logic.
More importantly, this question is not about the past, but about the near future, as it concerns a radical correction of quantum matrix mechanics, leading to a globally updated and error-free quantum mechanics.
The Heisenberg-Born-Jordan matrix, the first consistent matrix formulation of quantum mechanics in 1925, is a bit strange. It states:
Ψ =√h
0 -i√1 0 0i√1 0 -i√2 0 . . .
0 i√2 0 -i√3 . . .
0 0 i√3 0 -i√4 . . .etc.
Let's call the quantum matrix Q1.
Clearly, the Heisenberg matrix Q1 is the energy operator of the quantum system, which means:
E = ∭Ψ^2 (x,y,z,t) dx dy dz. Where E is the total energy of the quantum system E (x,y,z,t) = ΨΨ* = Ψ^2.Where E is the total energy of the quantum system E (x,y,z,t) = ΨΨ* = Ψ^2.Equation Q1 indicates that this imaginary equation, called the Heisenberg matrix mechanics equation, describes the square root of the energy density of the mechanical system, not the energy density itself. It is clear that the three giants of the time omitted two fundamental elements that characterize the difference between classical physics and quantum physics. [The statistical theory of Cairo techniques, which is natural intelligence], suggests the following two essential improvements:
i- Transition quantum mechanics must follow the sawtooth model.
ii- The correct transition quantum matrix, multiplied by the sawtooth vector state, yields the same sawtooth vector.
1- This means that the energy density of the sawtooth vector state is the stationary solution of a free quantum system (Dirichlet boundary condition = 0 and source/sink term S = 0), as in the case of an infinite potential well.
2- The correct transition quantum matrix, multiplied by the quadratic potential of the hydrogen atom, yields the same quadratic vector potential.
This means that the Nil Bohr hypothesis of quantization of angular momentum mv 2 Pi r (mv 2 Pi r = nh, n = 1, 2, 3 at infinity) is not essential for finding the energy levels of the hydrogen atom.
The correct squared magic sawtooth Q matrix for 1D 17 equidistant free nodes is given by,
166/2187 244/2187 266/2187 140/2187 35/2187 0 0 0 0 0 0 0 0 0 0 0 0
427/4374 853/4374 434/2187 322/2187 245/4374 35/4374 0 0 0 0 0 0 0 0 0 0 0
133/1458 124/729 343/1458 2/9 205/1458 10/243 5/1458 0 0 0 0 0 0 0 0 0 0
175/4374 230/2187 5/27 373/1458 355/1458 280/2187 55/2187 5/4374 0 0 0 0 0 0 0 0 0
35/4374 70/2187 205/2187 142/729 211/729 194/729 227/2187 26/2187 1/4374 0 0 0 0 0 0 0 0
0 5/1458 5/243 56/729 97/486 505/1458 205/729 50/729 5/1458 0 0 0 0 0 0 0 0
0 0 5/4374 22/2187 227/4374 410/2187 1981/4374 584/2187 43/1458 0 0 0 0 0 0 0 0
0 0 0 1/4374 13/4374 50/2187 292/2187 2849/4374 827/4374 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 827/4374 2849/4374 292/2187 50/2187 13/4374 1/4374 0 0 0
0 0 0 0 0 0 0 0 43/1458 584/2187 1981/4374 410/2187 227/4374 22/2187 5/4374 0 0
0 0 0 0 0 0 0 0 5/1458 50/729 205/729 505/1458 97/486 56/729 5/243 5/1458 0
0 0 0 0 0 0 0 0 1/4374 26/2187 227/2187 194/729 211/729 142/729 205/2187 70/2187 35/4374
0 0 0 0 0 0 0 0 0 5/4374 55/2187 280/2187 355/1458 373/1458 5/27 230/2187 175/4374
0 0 0 0 0 0 0 0 0 0 5/1458 10/243 205/1458 2/9 343/1458 124/729 133/1458
0 0 0 0 0 0 0 0 0 0 0 35/4374 245/4374 322/2187 434/2187 853/4374 427/4374
0 0 0 0 0 0 0 0 0 0 0 0 35/2187 140/2187 266/2187 244/2187 166/2187
It's easy, you can show it,
1-Q1 . [1 2 3 4 5 6 7 8 9 8 7 6 5 4 3 2 1 ] T = [1 2 3 4 5 6 7 8 9 8 7 6 5 4 3 2 1] T
---
2- For the case :
Q1 . [quadratic quantized atomic potential vector of hydrogen] = [Same quadratic quantized atomic potential vector of hydrogen]
with a relative error of less than 10%.
We begin by defining and presenting the statistical theory of Cairo techniques and its B-transition matrix chains, and assert that it is the universal unified field theory.
There are no partial differential equations, no classical mathematics, classical differentiation/integration, or anything else from classical R^4 space (3D geometry with real-time as an external controller) involved here.
All classical and quantum physics, as well as classical mathematics, are replaced by statistical matrix mechanics.
In other words,
It is true that Cairo intelligence techniques = natural intelligence = artificial intelligence in the strict sense = unified field theory.
The Heisenberg matrix mechanism is truly flawed. It is neither a transition matrix nor a statistical matrix, but it can be improved.
The statistical theory of Cairo techniques has been working effectively since 2020, that is, for four years, to numerically solve:
1- Time-dependent PDEs of classical physics in their most general form, such as LPDE PDEs, PPDE PDEs, and heat diffusion PDEs;
2- Time-dependent PDEs of quantum physics in 1D, 2D, and 3D;
3- Pure mathematics of differentiation/integration and classical and quantum statistical distributions, etc.
We show that the quantum physics transition matrix Q is the square root of the classical physics transition matrix B.
Q=√B.
It follows that, Q is essentially a complex matrix, but its energy eigenvalues are all real.
1- The elements of a quantum transfer matrix are all non-rational, but their square roots are such that √2, √3, √5, √10, etc.
2- The solution to the quantum system follows a sawtooth structure.
3- The geometry of a right-angled sawtooth structure implies that:
1111111 x 1111111 = 1234321 and 1111 x 11111 = 12321, etc.
The only flaw in this theory is that it reveals the errors of the scientist Niels Bohr, which displeases both Bohr's iron guards and their followers.
They were nursed and weaned by Bohr and his followers, and the probability of their recovery is less than a few percent.
You can also obtain the quantum transition matrix Q without resorting to the formula Q=√B:
For 17 free 1D QM nodes, start with the sawtooth form of the outer product of,
[1 2 3 4 5 6 7 8 9 8 7 6 5 4 3 2 1]T
⊗
[1 2 3 4 5 6 7 8 9 8 7 6 5 4 3 2 1]
You finally obtain the 1D quantum transition matrix with the sawtooth form,
The geometry of a right-angled sawtooth structure implies that,
1111111 x 1111111 = 12345654321
and
1111 x 1111 = 12321, etc.
Note that all the above numerical values are expressed as dimensionless arithmetic numerical values.