>>13627041QM is filled with the evidence of being a hobbled together pile of shit. This is a more advanced topic, tho. Schrodinger was trying to create an equation to match DeBroglies dispersion relations equations, and behave like a wave.
This is not a trivial task. It would have been amazing if he could have done it. The problem is a normal wave equation will yield a linear dispersion relation equation. Sound and EM are linear dispersion in free space. Electrons were known to have quadratic dispersion. This proved to big problem for schrodinger. If he wrote the time derivative term to be first order, then he wouldn't get oscillating solutions, they would have been exponential. If he used a second order derivative for the time derivative term he would be stuck with linear dispersion, contrary to what De Broglie said. Schrodingers solution is pure hack. He kept the first order time derivative to get the right dispersion relation, but multiplied that time derivative by sqrt(-1) or the imaginary unit. This meant that the solutions would be exponential, but that exponent would be imaginary and therefore oscillate like a wave, which is what he originally needed. The only problem remaining is all his solutions were now complex.
But here is the ever present question: IS THIS PHYSICS? tooling around with maths to get the expression you want? When you don't get the expressions you want inventing rules to make it seem less incorrect, and fiddling with the interpretation to make it seem more real.
My answer is this is just terrible physics, statistics and math jammed together. It's an abomination.
It's not physics because there is no physical property involved
It's shitty probability because it's all complex and negative
It's shitty math, because he failed to derive an equation that fit the application.
