Some Iron Guard mathematicians and physicists have argued for nearly a century that it is an idol that should never be touched.
On the other hand, for each in-depth question in quantum mechanics they refer to SE and its derivatives to obtain coherent or incoherent answers from Google or elsewhere which often do not allow the questioner to advance a centimeter.
In fact, they didn't understand SE simply because it's not understandable.
These are not my words but these are the words of the giant N. Bohr who invented quantum wave superposition as the only interpretation of SE.
We assume that SE can be greatly improved if it could be rewritten into a 4D inseparable x-t space.
It would be useful to learn quantum mechanics, before making claims that don't make sense.
Bohr was confused about many issues, what matters are the issues he wasn't confused about.
The Schrödinger equation describes the evolution of the wwve function. The independent variables are the position coordinates and time. So it's a standard exercise to solve it for the wavefunction of a particle that explores a three-dimensional space. For a relativistic particle the only thing that changes is the expression of the Hamiltonian operator.
This is just an introductory response to thank our French colleague for his helpful response.
He recommends learning the Schrödinger equation (SE) before making statements that make no sense.
his response alone backfires.
1- He admits that the great Bohr only understood half of the SE, but we further assume that another winner of the Most Brilliant Noble Prize, "R, Feynman", also understood nothing and issued the statement: Shut up and calculate.
Forget Bohr and Feynman though, because our colleagues claim to understand a lot about SE - Note that nothing outside of SE is important?
2- It admits that SE is a wave function of a particle which explores a three-dimensional space.
Three-dimensionality is the main disadvantage of SE.
3- Our claim to rewrite the SE in a 4D unit space xt does not come from scratch but is predicted by the theory of matrix mechanics.
The theory of matrix mechanics has been shown to be capable of numerically solving classical time-dependent physics 3D-PDE, QM PDE and even mathematical integration ∫∫∫ f(x,y,z) dx dy dz.
Therefore, we logically assume that SE is a subset of matrix mechanics and not the other way around.
4-It is absurd to assume that the missing physical parts in SE can be completed by SE itself?
Please take a look at,
Fall and rise of matrix mechanics.
Researchgate, January 2024.
IJISRT, January 2024.
We hope that it will provide detailed answers to the interested reader.
It's a standard exercise that the properties of the phase space of a physical system described by the Schrödinger equation are the same-nothing more and nothing less-than the properties of the phase space of a physical system using matrix mechanics. And both are equivalent to the path integral formalism. There's nothing wrong with any of them-it's just that, for many problems, solving Schrödiger's equation requires doing much simpler calculations than using matrix mechanics. There are other problems where the opposite is true. And there are other problems where the path integral formalism is more convenient.
All three are discussed in any textbook these days. And any formalism is only useful for solving problems. It doesn't matter which one is used, what matters are the problems that are solved.
What proclamations about ``fall and rise'' show is, just, ignorance.
Use whatever formalism to solve problems that are relevant now!
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