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Sep 30, 2014 at 18:23 comment added Nikos M. @ChrisGerig, om its your choice, for my defense i will simply say that the first part relates to tge Dirac quote on your question and the second part relates (at least that is the motivation) to the last part of your question hinting at simple systems "But what are some examples (and consequences) of elementary dynamical systems whose quantum Hamiltonian differs from its classical Hamiltonian?". For specific elementary systems which have factors of the form $p^mx^n$ there are some examples in curved spaces (there are others also)
Sep 30, 2014 at 17:08 comment added Chris Gerig This doesn't answer my question at all. I know what the problem is; and the last paragraph cheats in a way (it's not in the spirit of Dirac's remark).
Sep 30, 2014 at 11:24 history answered Nikos M. CC BY-SA 3.0