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I was trying to help (elsewhere) a student with some QM related problem and I realized something. When discussing QM we underline the fact that electron doesn't behave as a particle, it behaves as a wave. Yet when we explain wave function we say something like "square of the wave function is a density probability of finding the electron" - which seems to suggests to students the electron is a particle that can be found in a given place with a given probability. I feel like it enforces thinking in terms of electron being a pointlike object and as such doesn't help students in understanding the subject.
Won't it be better to explain these things in terms of the charge density? Unless I am missing something very fundamental, charge density and probability density of finding electron are directly proportional to each other, so we are free to choose whether we call the square of the wave function "probability density" or "charge density", aren't we?
Sadly, fact that every QM textbook I know uses the same "probability density" approach probably renders the idea DOA.
(I am actually not sure where is the best place to discuss it, feel free to move the thread).
Won't it be better to explain these things in terms of the charge density? Unless I am missing something very fundamental, charge density and probability density of finding electron are directly proportional to each other, so we are free to choose whether we call the square of the wave function "probability density" or "charge density", aren't we?
Sadly, fact that every QM textbook I know uses the same "probability density" approach probably renders the idea DOA.
(I am actually not sure where is the best place to discuss it, feel free to move the thread).