Remeasurement of a quantum system

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Discussion Overview

The discussion revolves around the behavior of a quantum system following a measurement, specifically addressing the wavefunction collapse and the subsequent measurements of dynamical variables. Participants explore the implications of repeated measurements and the evolution of the wavefunction over time.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant states that after a measurement, the wavefunction collapses into the corresponding eigenfunction and questions why subsequent measurements yield the same results and probabilities.
  • Another participant suggests that the wavefunction slowly starts spreading out again after the measurement.
  • A participant seeks clarification on the reasoning behind the eigenvalues remaining the same upon repeated measurements and references a question from a book that prompted this inquiry.
  • One participant introduces the concept of information and describes the time evolution of the state using a propagator, indicating that the probability of observing a state is related to the overlap integral between initial and final states.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the reasons behind the behavior of the wavefunction and the consistency of measurement results. Multiple viewpoints are presented without a consensus on the underlying mechanisms.

Contextual Notes

The discussion includes assumptions about the nature of wavefunction collapse and time evolution, as well as the dependence on specific definitions of eigenfunctions and measurements. Some mathematical steps and reasoning remain unresolved.

Who May Find This Useful

Individuals interested in quantum mechanics, particularly those exploring the implications of measurement theory and wavefunction behavior in quantum systems.

swain1
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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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I think it slowly starts spreading out again.
 
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?
 
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
 

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