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Re:Is the Schrödinger Equation True? by ur-whale on Tuesday January 12, 2021 @08:06AM (#25746273)
> There's a discontinuous boundary?

I don't think he's claimed that the boundary was discontinuous, you've implied that.

However, there's no denying that QM and classical mechanics are two fairly different sets of equations.

I haven't come across a QM book so far that explicitly (i.e. with an example) demonstrates how one morphs into the other as a variable, say size, changes.

Special relativity is way better in that regard, when speed goes to zero, the equations converge to their classical analogues.

Re:Is the Schrödinger Equation True? by kirrent on Tuesday January 12, 2021 @04:16PM (#25753805)
> I haven't come across a QM book so far that explicitly (i.e. with an example) demonstrates how one morphs into the other as a variable, say size, changes.

Ehrenfest's theorem would be an example where Newton's 2nd law is recovered as the wavefunction's spatial extent is reduced on the scale of the system being studied. More generally, you won't get an explanation that shows a morphing based on size because size is not the limiting factor. It's how isolated your system can be from the outside world. This is obviously much much harder as your system gets bigger. Decoherence theory (https://en.wikipedia.org/wiki/Quantum_decoherence) recovers classical probabilities as a system interacts with its environment.