Since there cannot be zero momentum in QM systems do such things as Zitterbewegung imply accelerations?
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1See Is Zitterbewegung an artefact of single-particle theory?. Zitterbewegung is not to be taken literally as the particle vibrating to and fro. – John Rennie Dec 10 '14 at 12:07
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However, there is still zero point motion in other systems due to the uncertainty principle. Does that involve accelerations? Or only on measurement? – Dec 10 '14 at 13:05
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1Re the close as duplicate vote, Dirk's question is clearly broader than just Zitterbewegung, so the question Is Zitterbewegung an artefact of single-particle theory? is not a duplicate. – John Rennie Dec 10 '14 at 14:19
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Forget Zitterbewegung. It's about motion of particles in lowest energy states, including (say) liquid helium. – Dec 10 '14 at 15:12
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Dirk, I'm not sure your question as sense, as I suspect you are still thinking about the oscillator as if it was a classical particle. If you express a SHO in momentum space then the ground state is something like $\Phi(p,t) = A \exp(-p^2/2\hbar m \omega - i\omega t/2)$ so it's not a momentum eigenstate, but the momentum isn't changing in any oscilliatory way as it would in a pendulum. – John Rennie Dec 10 '14 at 16:14