What is the Explanation for the Double Slit Experiment in Quantum Mechanics?

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Discussion Overview

The discussion centers on the explanation of the double slit experiment within the framework of quantum mechanics (QM). Participants explore the nature of wave functions, their evolution, and the implications of barriers in the context of quantum behavior, touching on theoretical and conceptual aspects of QM.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant asserts that the double slit experiment is explained in QM through the superposition of two wave functions, each corresponding to one of the slits.
  • Another participant notes that the type of wave function entering the double slit depends on the specific situation, suggesting it could be a plane wave or spherical wave.
  • A participant expresses confusion regarding the relationship between solutions to the Schrödinger equation (SE) and measurements, questioning how non-linear events like collisions fit into the linear framework of the SE.
  • Concerns are raised about how barriers affect the wave function, particularly in scenarios with single or double slits, and how this relates to the mathematics governing the SE.
  • A later reply references a paper by T.V. Marcella, questioning the common explanation of the double slit experiment and suggesting alternative perspectives.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the explanation of the double slit experiment, with multiple competing views and interpretations presented throughout the discussion.

Contextual Notes

There are limitations in the discussion regarding the assumptions about wave functions and the specific conditions under which they are analyzed. The relationship between the SE and non-linear events remains unresolved, as does the impact of barriers on wave functions.

wofsy
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the double slit experiment is explained in QM as the superposition of two wave functions. Each is the wave function for one of the slits.

an electron starts out with a wave function that is clustered near the point of emission and then evolves on some way according to the Shroedinger equation. What is this wave function? How does the slitted barrier modify say a wave function that would otherwise have been Gaussian?
 
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It is hard to give you a specific answer since you are asking what kind of wave function is entering the double slit; it depends on what situation you have I would say. It could be a plane wave, spherical wave etc.

Assuing the double slit is beeing illuminated by a current of particles with plane waves, the distortion of this wave "is done" in the same way as with classical waves. The non relativistic quantum mechanics formalism is basically wave physics mixed with probability theory (and other stuff such as Functional analysis etc)
 
Glenn

thanks so much for your help.

I guess the source of my questions was this underlying idea that there are only two things that happen in QM, solutions to the SE and measurements.

Solutions to the SE are solutions of linear equation and so can not explain measurements.

On the other hand there are superficially non-linear events such as collisions which can not possibly be solutions of the SE and I was trying to see what really happens so that the SE is obeyed.

The double slit seems related to this because if there is no slit then there is a barrier that prevents the electron from passing through to the detecting screen so this barrier must affect the wave function/interact with the electron somehow. With a single slit the barrier must still be at work except now it has an escape hole. The mathematics of this situation is what I was after since the SE is the only thing at work.

Again, thanks for your help.
 
wofsy said:
the double slit experiment is explained in QM as the superposition of two wave functions. Each is the wave function for one of the slits.

Does it really? Read the Marcella paper:

T.V. Marcella Eur. J. Phys. v.23, p.615 (2002). The preprint http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf" .

Zz.
 
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