Monday, 1 October 2018

quantum mechanics - Why does the Heisenberg uncertainty principle refer to momentum rather than velocity?


I've been looking at the Heisenberg uncertainty relations, and something that sticks out to me is the use of momentum rather than velocity. Shouldn't electrons have the same mass? And if they do, why is momentum used?




Answer



Because the uncertainty principle applies to all particles, regardless of their mass (and even for some massless particles). Thus, you could, if you insisted, phrase the uncertainty principle for electrons as ΔvΔx12me

and the uncertainty principle for protons as ΔvΔx12mp
and the uncertainty principle for neutrons as ΔvΔx12mm
and the uncertainty principle for helium atoms as as ΔvΔx12mHe
and so on and on and on, but why would you do that when you can just issue a single principle that applies for all particles, ΔpΔx12,
and be done with it?


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