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I am taking an introductory course on quantum mechanics and would like to understand this. Do forces act in quantum mechanics? In orbitals, is the charge of an electron dispersed, with a higher charge at places with a higher probability of finding an electron? Is there any centripetal force/acceleration at the quantum mechanical level? Thank you.

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    $\begingroup$ Short answer to your charge question: no it's not dispersed. I believe that was actually the first attempt at interpreting the wave function, as a spatial charge density over a volume, but this was quickly found to be incorrect. Then came the probability interpretation, that the square of the wave function represents a probability density of finding a point charge at a given location. $\endgroup$ – David H Sep 5 '13 at 5:52
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In quantum mechanics the charge of the electron is always "concentrated" at a single point. What happens, for instance to compute effective interactions, is that effectively the charge may be thought of as dispered due to the probability density of the electron (given by its wave function) to carry out specific computations, as in effective field theories. On the other hand the concept of "force" as seen in Newtonian or classical mechanics, ceases to exist in quantum mechanics. It is replaced by the concept of interaction, or interaction potential. In quantum mechanics there are no "spatial trajectories" as un classical mechanics, so one cannot talk about acceleration of a particle or force.

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