Can someone explain why momentum does not commute with potential?

In summary, momentum is the measure of an object's motion while potential is the stored energy of an object based on its position or configuration. In quantum mechanics, momentum and potential are non-commuting operators, meaning their order of operation affects the outcome of the calculation. This is known as the Heisenberg uncertainty principle, which has significant implications in the behavior of subatomic particles and leads to the probabilistic nature of quantum mechanics. The double-slit experiment is an example of momentum not commuting with potential, as the act of measuring one disturbs the other. This relates to the uncertainty principle, which places a fundamental limit on our ability to accurately measure physical quantities such as position and momentum simultaneously.
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coolpoke0908
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So I only have a vague understanding of what commutators represent. I understand the example between momentum and position, but I don't understand why you cannot know the potential and the momentum of a particle at the same time.
My assumption is that knowing potential can lead to knowing the position, but I don't know how this can be.
 
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  • #2
If by "potential" you mean "potential energy as a function of position", there is a clue right there.
 
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Vanadium 50 said:
If by "potential" you mean "potential energy as a function of position", there is a clue right there.
Oh! Okay that makes sense! Thank you!
 

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