Wavefunction After Measurement

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SUMMARY

The discussion centers on the behavior of wavefunctions after measurement in quantum mechanics, specifically using the example of a superposition of energy eigenfunctions, ψ(x)=(1/√2)*(ψ1+ψ2). Upon measuring the energy E1, the wavefunction collapses to ψ1, eliminating the superposition. The participants confirm that after this collapse, the wavefunction becomes time-independent, simplifying to ψ=φ1, with the time-dependence represented as a global phase rotation.

PREREQUISITES
  • Understanding of quantum mechanics principles, particularly wavefunction collapse.
  • Familiarity with energy eigenfunctions and superposition states.
  • Knowledge of measurement theory in quantum mechanics.
  • Basic grasp of time evolution in quantum systems.
NEXT STEPS
  • Study the implications of wavefunction collapse in quantum mechanics.
  • Explore the concept of superposition and its role in quantum states.
  • Learn about measurement theory and its interpretations, including the Copenhagen interpretation and Many-Worlds Interpretation (MWI).
  • Investigate the mathematical representation of time evolution in quantum systems.
USEFUL FOR

Students and professionals in physics, particularly those focusing on quantum mechanics, wavefunction behavior, and measurement theory.

kingzeon
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Forgive me for asking such a basic question but say for IDSW1 if we have a wavefunction that is a superposition of the first two energy eigenfunctions so:

ψ(x)=(1/√2)*(ψ1+ψ2)

then if we measured say E1 we can eliminate the inconsistent part of the wavefunction so the wavefunction collapses to ψ1. Then directly after, and also some time later, will the wavefunction be independent of time so we can in fact simplify the wavefunction to ψ=[itex]\phi[/itex]1?

Thanks in advance
 
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You (with collapse or similar interpretations) or the part which measures 1 (with MWI) can describe the state as stationary with wave function 1, correct. The time-dependence is just a global rotation of the phase.
 

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