How can the particle fit in the well then?

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Discussion Overview

The discussion revolves around the concept of a particle in an infinite square well potential, specifically addressing the apparent contradiction of a particle's wavelength being twice the length of the well while fitting within it. The scope includes theoretical aspects of quantum mechanics and wavefunctions.

Discussion Character

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

Main Points Raised

  • One participant questions how a particle can fit in a well when its ground state wavelength is twice the length of the well, suggesting a misunderstanding of the relationship between wavelength and particle size.
  • Another participant clarifies that the wavelength refers to the wavefunction of the particle, which is a mathematical representation of the particle's state, not the particle itself.
  • A different participant emphasizes that the wavefunction describes the probability of locating the particle and notes that the particle is typically treated as a point particle in quantum mechanics.
  • One participant reiterates the initial question about the particle fitting in the well and draws an analogy to a classical vibrating string, explaining that the fundamental mode of vibration has a wavelength twice the length of the string.
  • This same participant argues against the notion that the wavelength must correspond to the size of the particle, stating that it is not necessary to have a whole particle fit within a wavelength.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of the wavefunction and its implications for the particle's size and behavior within the well. The discussion remains unresolved with multiple competing perspectives on the relationship between wavelength and particle fitting in the well.

Contextual Notes

There are limitations in the assumptions made about the nature of the wavefunction and the interpretation of quantum mechanics, particularly regarding the distinction between the mathematical representation and physical properties of particles.

touqra
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In an infinite square well potential, the ground state of a particle, has a wavelength twice the length of the well. How can the particle fit in the well then? It's not even one wavelength.
 
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When you say the particle['s]...wavelength, I think you mean the wavelength of the particle's wavefunction. Please understand the fundamental difference between the two things.

The wavefunction of the particle is (at the very least) a mathematical object representing all we can know about the state the particle is in. To determine other properties of the particle, you must perform measurements of dynamical variables of the system.
 
The wavefunction describes the probability of finding a particle in a given interval, the particle is usually considered to be a point particle. Eh, at least in the problems I've worked out so far.
 
touqra said:
In an infinite square well potential, the ground state of a particle, has a wavelength twice the length of the well. How can the particle fit in the well then? It's not even one wavelength.

The wave function is zero in the middle of each full wavelength, which matches the value it must have outside the box.

If you have a classical vibrating string with fixed ends, the fundamental mode of vibration (the one with lowest frequency) has a wavelength that is twice the length of the string, for exactly the same reason.

If you're thinking that the wavelength has to do with particle size, and you can't have half a particle, therefore you can't have half a wavelength, that's not so.
 

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