[bollu]

What do you mean by "derive" the Schrödinger equation? As best as I know, there is no "derivation" beyond some analogy with the classical wave equation. It's an equation penned down by Schrödinger, motivated by the classical wave equation and insights from de broglie's theory.

I'd love to see a derivation if it exists.

[sls]

I have in mind things like this [1]. I no longer have my undergraduate text or notes but I recall going through a similar exercise.

[1] https://arxiv.org/pdf/physics/0610121.pdf