Undergrad Can someone explain why momentum does not commute with potential?

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Momentum does not commute with potential because potential energy is dependent on position, which affects the system's dynamics. Understanding potential energy as a function of position provides insight into how momentum interacts with forces. The relationship between potential and momentum highlights the non-commutative nature of these quantities in physics. This discussion emphasizes the importance of recognizing the role of potential energy in determining the behavior of particles. Overall, the interplay between momentum and potential is crucial for understanding physical systems.
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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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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!
 

Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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