Quantum Mechanics: Measuring Position and Momentum

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In summary, the conversation is discussing the relationship between measuring the position and momentum of a system, and how the accuracy of the position measurement affects the momentum measurement. The question also arises about whether the momentum will be represented by a specific equation or if it will be constant for all values of k.
  • #1
bodensee9
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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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  • #2
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.
 
  • #3
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?
 

Related to Quantum Mechanics: Measuring Position and Momentum

1. What is the uncertainty principle in quantum mechanics?

The uncertainty principle states that it is impossible to know the exact position and momentum of a particle simultaneously. The more precisely one is known, the less precisely the other can be known. This is due to the wave-like nature of particles in quantum mechanics.

2. How is position measured in quantum mechanics?

In quantum mechanics, position is measured by finding the probability of a particle being located at a certain point in space. This is done using mathematical equations and operators to describe the position of the particle.

3. What is momentum in quantum mechanics?

Momentum is a measure of an object's motion in quantum mechanics. It is described by the product of an object's mass and velocity and is used to calculate the object's energy and behavior in quantum systems.

4. How is momentum measured in quantum mechanics?

Similar to position, momentum is also measured by finding the probability of a particle having a certain momentum. This is done using mathematical equations and operators to describe the momentum of the particle.

5. How does the act of measuring position or momentum affect the particle in quantum mechanics?

In quantum mechanics, the act of measuring a particle's position or momentum can actually change the state of the particle. This is known as the observer effect and is a fundamental aspect of quantum mechanics.

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