Can someone tell me if there is a difference in the moving motion between a quantum harmonic oscillator and a simple harmoic oscillator. Also, does anoyone know a good site where i could learn more on quantum harmonic oscillator.
If you mean, how does the particle "actually move" in a quantum harmonic oscillator, the answer is the same as for an electron in a hydrogen atom, etc. QM gives us the probabilities for finding the particle at various locations (or the values of other physical quantities such as energy, momentum, etc.) when we observe/measure it, but it does not tell us what it is "actually doing" before we observe/measure it.
This is the subject of interpretations of QM (Copenhagen, Bohmian, many-worlds, etc.). They all make (so far) the same predictions for the probabilities that we can actually observe/measure, so there is no way (as yet) to distinguish between them experimentally. People argue endlessly about which interpretation is best, based mainly on personal philosophical and metaphysical preferences, on this forum and elsewhere.