It is not possible to derive Schrödinger’s equation from “anything we know”.
— R. P. Feynman
The most confusing part in the Quantum Mechanics is [the concept of] Trajectory.
There exist[s] no fixed path for a particle to go from Point A to Point B. This is clearly visible from [the] Interference Experiment.
So, the approach here is to work with deductive reasoning. We eliminate the possible region/paths which [are] impossible to be followed.
To do this we assume that Energy Conservation Relation is valid for Quantum Mechanics too. So, those regions where particle[s] [violate] this law automatically [get] eliminated.
Then, we guess [the] State Function[s] for certain conditions i.e. how it should be in certain cases, then build an energy conservation equation with that. We will shortly demonstrate how Schrodinger itself reached the conclusion.
— Why can’t the Schrödinger equation be derived?
— Abhas Kumar Sinha
2021.02.28 Sunday ACHK