Is the Uncertainty Principle the Key to Solving Homework Problems?

AI Thread Summary
The discussion centers on the application of the uncertainty principle in solving homework problems related to quantum mechanics. The user questions whether the uncertainty principle applies to observables with specific commutators, particularly [p, V(x)] and [x, H]. They suggest that both questions posed in the homework may have affirmative answers based on their calculations. The user seeks clarification on whether the uncertainty principle is valid only for observables with commutators equal to ±ih/2π. The conversation emphasizes the importance of understanding commutators in the context of quantum mechanics.
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Homework Statement


See q attached



Homework Equations





The Attempt at a Solution



Am i right in thinking that the answer to both questions is yes? Neither of the commutators [p, V(x)] nor [x, H = + or - ih..

therefore is the answer to both a and b yes?
 

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The thing is that [p, V(x)] gives -ih/2pi DV/DX where D/Dx is partial d/dx..

does the uncertainty principle only hold between oberservables whose commutator = plus or minus ih /2pi?

Thanks
 
Can anyone help with this?
 

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