Hi Ismail,

Here is a link to a Python visualization of the probability density function of an electron in a 3D box based on the Schrödinger equation that you might find it worth exploring.

https://github.com/mohamadasadizade/quantum_particle

We first show that the space of Cairo techniques is complete while Schrödinger's construct is not:

let's return to pragmatic philosophy:

i- When the space that we propose solves all the problems of classical and quantum physics in addition to mathematics, then this space is true and complete and its adversaries are wrong.

ii- When the space proposed by Schrödinger does not solve all the problems of classical and quantum physics in addition to mathematics, then this space is neither complete nor correct.

Therefore, the interpretation of Schrödinger's PDE often leads to common errors: (1) confusing the wave function ψ(x,t) with a physical wave, when it is a probability amplitude; (2) ignore its probabilistic nature, because ∣ψ∣2 gives a probability density, and not deterministic trajectories; (3) poor understanding of the role of the Hamiltonian in governing energy dynamics and eigenvalues; (4) neglecting boundary conditions and normalization, which are essential to physical solutions; (5) neglect the importance of the complex nature of the wave function, because its phase is critical for quantum interference and superposition and

(6) the wave function in QM PSI is continuous but its derivative is not continuous?

In physics textbooks it is written that the Psi wave function and its first derivative must be continuous.

Meanwhile, in these same books you find many situations where the Psi solution is continuous and its derivative is not, the simplest example is the particle in a one-dimensional box.

It is almost impossible to avoid these errors since they are inherent in SE with the Bohr-Copenhagen interpretation.

Schrödinger's first slip was to formulate his QM wave equation and deduce entanglement as an implication when the opposite is more true.

The entanglement between space and time is a universal law of physics.

However, we believe that E. Schrödinger had a deep understanding of quantum mechanics.

Only, he did not have the power to impose his own ideas against the giants of the time , N. Bohr, Heisenberg, Einstein, etc.

Check out his brilliant quotes:

I-entanglement is not one, but rather a characteristic of quantum mechanics.

ii- He declared,

“I don’t like it and I’m sorry I ever had anything to do with it.”

Today, after 100 years, we are more reliable about what is true and what is false.