Wavefunction after position measurement

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Discussion Overview

The discussion revolves around the behavior of a particle's wavefunction following a position measurement, specifically within a confined region on the x-axis. Participants explore the implications of measuring a particle's position within a specific interval and the resulting changes to the wavefunction, considering both cases of finding the particle within the interval and not finding it there.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant proposes that if a particle is measured to be within a small interval [a, b], the wavefunction would collapse into a rectangle-like function with equal probability density in that interval and zero outside.
  • Another participant questions the nature of the measurement, suggesting that if the measurement device indicates the particle is between a and b, the wavefunction collapses to a Dirac Delta function at the measured position if the actual position is determined.
  • It is suggested that if the particle is not found in the interval [a, b], the wavefunction must become zero in that region, but the exact form of the wavefunction afterward remains unclear.
  • There is a mention that regardless of the measurement outcome, the wavefunction will quickly evolve according to the Schrödinger equation.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the wavefunction collapse and the effects of measurement, indicating that multiple competing perspectives remain unresolved.

Contextual Notes

Participants do not fully clarify the assumptions regarding the measurement process or the initial form of the wavefunction, leaving some aspects of the discussion dependent on these definitions.

MHD93
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Suppose I have a particle confined between 0 and d on the x axis, and it has some wavefunction, if I measured the particle to be between some small interval [a, b], would the wavefunction collapse into a rectangle-like function with equal prob. density on the interval and zero outside? or what?

Suppose, instead, that I measured the region [a, b] and did NOT find the particle there, it is reasonable that the wavefunction would be affected (i.e. it must become zero on [a, b]). Right or wrong? and if right how will it look like?
 
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What do you mean by measure the particle in some small interval? Do you mean you have some measuring device that if the particle is between a and b returns yes? Or do you mean you have a measuring device that will tell the actual position between a and b? If the former then yes if the latter it will collapse to a Dirac Delta function at the measured position.

If you measure it and under either scenario its not between a and b then it will collapse to a wave-function that is zero between the area you measured the position.

Under both scenarios it will quickly spread via the Schrodenger equation.

Thanks
Bill
 
Do you mean you have some measuring device that if the particle is between a and b returns yes?
Yes, I am talking about this.

...it will collapse to a wave-function that is zero between the area you measured the position
and elsewhere? this is my question.
 
Mohammad_93 said:
and elsewhere? this is my question.

What it was before - but that will quickly collapse into the solutions of a particle in the box via the Schrödinger Equation.

Thanks
Bill
 

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