Remeasurement of a quantum system

In summary, after making a measurement of a particular dynamical variable, the wavefunction collapses into the corresponding eigenfunction. When the variable is measured again, the results and relative probabilities of eigenvalues remain the same as before. This is because the wavefunction slowly starts spreading out again, as described by the propogator which dictates the time evolution. The probability of observing a state at a later time is determined by the overlap integral between the initial and final state. Therefore, the eigenvalues will be the same when another measurement is made due to the spreading out of the wavefunction.
  • #1
swain1
30
0
After making a measurement of a particular dynamical variable the wavefunction collapses into the corresponding eigenfunction. As I understand when the variable is then measured again the results and relative probabilities of eigenvalues are exactly the same as before. I don't understand why they are the same as before. What happens to the wavefunction?
 
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  • #2
I think it slowly starts spreading out again.
 
  • #3
ok. Why does it spread out though? Is there a reasoning behind why the eigenvalues will be the same when another measurement is made. There was a question in a book that kind of asked for an answer to this but I can't work out why?
 
  • #4
Information. Start out with a state described by an eigenfunction then apply the propogator to it which describes the time evolution. At a later time the probability of observing some state is proportional to the overlap integral between the initial and final state...to put it simply
 

FAQ: Remeasurement of a quantum system

1. What is remeasurement of a quantum system?

Remeasurement of a quantum system is the act of measuring a specific observable property of a quantum system multiple times in order to obtain a more accurate measurement of that property.

2. Why is remeasurement important in quantum systems?

Remeasurement is important in quantum systems because the act of measuring a property can change the state of the system, and by remeasuring the same property multiple times, we can obtain a more precise understanding of the system's state.

3. What are the limitations of remeasurement in quantum systems?

The limitations of remeasurement in quantum systems include the fact that each measurement can still have a small amount of uncertainty, and the act of measuring can disturb the system's state, making it difficult to obtain completely accurate measurements.

4. Can the results of remeasurement be predicted in quantum systems?

In quantum systems, the results of remeasurement cannot be predicted with certainty due to the inherent probabilistic nature of quantum mechanics. However, the probability of obtaining a certain result can be calculated using mathematical equations.

5. How does remeasurement contribute to our understanding of quantum mechanics?

Remeasurement contributes to our understanding of quantum mechanics by allowing us to obtain more accurate measurements of quantum systems, which in turn can help us better understand the underlying principles and behaviors of these systems.

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