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why most quantum mechanics tools are derived from classical mechanics ? (and everything is ok)

why we can do a safe jump from classical scalar quantities (Hamiltonian, momentum, angular momentum, spinning charge in a loop) to quantum operator quantities (Hamiltonian, spin.. ) using basic calculus.

a lot of confusing ideas are here, like : the electron isn't really spinning but the derivation of the quantum magnetic moment by calculating the classical magnetic moment of a classical charge spinning in a circle leads to a true answer ..

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