Quantum Mechanics: Measuring Position and Momentum

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SUMMARY

The discussion focuses on the relationship between position and momentum measurements in quantum mechanics, specifically addressing the implications of measuring position at a specific value X. The integral presented, 1/sqrt(2*pi)* integral (exp(ikX))*(exp(-ikx))dx, is identified as undefined, prompting questions about the correct representation of momentum after a position measurement. The conversation emphasizes the importance of the measurement device and accuracy, noting that repeated measurements in cloud chambers do not significantly alter momentum. Clarification is sought on whether the inquiry pertains to immediate momentum measurement or the momentum-space representation post-position measurement.

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Homework Statement


Hi, Let's say that I measure the position of a system and I get that it is at X. So then if immediately after I measure the momentum, will I get:

1/sqrt(2*pi)* integral (exp(ikX))*(exp(-ikx))dx?
But this integral is undefined?
Then how do I find the momentum wave after measuring position? Thanks!

Or will my momentum just be exp(ikX)? for all range of K?

Thanks.
 
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That depends on how you measure the position - with which device and with which accuracy. In cloud chambers positions are being measured again and again, many times on the same particle, and nothing dramatic happens to the momentum.
 
Are you asking about actually measuring the momentum immediately after you measured the position of the system, or are you just trying to find the momentum-space representation of the state after the measurement?
 

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