Does Heisenberg apply to a collapsed wavefunction?

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SUMMARY

The discussion centers on the application of the Heisenberg Uncertainty Principle (HUP) to collapsed wavefunctions in quantum mechanics. Participants argue that HUP is fundamental and applies to both particles and waves, asserting that upon wavefunction collapse, the particle exhibits definite position and momentum. However, post-collapse, the particle reverts to a wave state, leading to uncertainty in its properties. The conversation emphasizes the need for a deeper understanding of quantum mechanics, particularly regarding non-commuting observables and the nature of wavefunctions.

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  • Understanding of the Heisenberg Uncertainty Principle (HUP)
  • Familiarity with wavefunction collapse in quantum mechanics
  • Knowledge of non-commuting observables in quantum mechanics
  • Basic principles of quantum mechanics, including wave-particle duality
NEXT STEPS
  • Study the implications of non-commuting observables in quantum mechanics
  • Explore the concept of wavefunction collapse and its interpretations
  • Investigate the mathematical formulation of the Heisenberg Uncertainty Principle
  • Read "Quantum Mechanics - A Modern Development" by Ballentine for foundational insights
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  • #31
kith said:
"Measurement" is not a purely physical term but is related to how a person acquires knowledge. If you remove the pointer from your amperemeter, you don't have a measurement apparatus anymore although the physical interaction between your system of interest and the amperemeter doesn't change.

This is part of the difficulty with the whole measurement paradigm of what QM is and why its a difficult issue.

Basically in modern times a measurement is replaced with dechoherence which is independent of pointers in measurement apparatus etc. But this is an advanced issue best glossed over for HS students.

Thanks
Bill
 
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  • #32
Hi,

And 'collisions' and 'particle-like-behaviour', are these more or less synonyms?

-> is there particle-like-behaviour that does not involve collisions?

Paul, who is grateful for al the responses.
 
  • #33
T'Pau said:
Hi,

And 'collisions' and 'particle-like-behaviour', are these more or less synonyms?

-> is there particle-like-behaviour that does not involve collisions?

Paul, who is grateful for al the responses.

Tricky, tricky, tricky.

Yes, collisions are particle like behaviour.

However, in LHC type collisions, the rough idea is that one sends in free, non-interacting particles, the particles collide and interact, and then the outgoing particles from the collision are again free, non-interacting particles. The tricky part is that a free particle from a collision is the most unlocalized state, because it is a particle with a definite momentum. Since it has a definite momentum, it must have very undefinite position. But then what about all those particle tracks? Well, although the tracks looks small and localized to us, they are big from the point of view of the uncertainty principle.

http://books.google.com/books?id=CNCHDIobj0IC&vq=particle&source=gbs_navlinks_s
p117: To a particle the beam is the whole universe, and it is big!
 

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