Do p and σz Commute?

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The discussion focuses on the commutation relationship between the momentum operator p and the Pauli spin matrix σz. The original poster is unsure how to approach the problem and initially suggests that the commutator might be zero since they operate in different spaces. Niles argues that specifying the direction of the momentum operator is crucial, noting that if measuring x-momentum indicates a specific state, it can influence the spin state. Ultimately, Niles concludes that the operators do commute, contradicting the initial assumption. The conversation emphasizes the importance of understanding the relationship between different quantum operators.
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Homework Statement


Hi

I want to find the commutator between the momentum operator p and σz, the third Pauli spin matrix. I am not quite sure how to get started on this one. Can I get a push in the right direction?

For the record, I would say that it is zero since they act on different spaces. Is this correct?


Niles.
 
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I think it's important to specify a direction for the momentum operator. I think that, if it's x-momentum and z-spin and you measure x-momentum to be zero every time then you know that the spin vector is probably in the x direction telling you for sure that z-spin is zero, meaning they don't commute.
 
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