No free particle in real world

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Discussion Overview

The discussion revolves around the concept of free particles in quantum mechanics, specifically questioning whether true free particles exist in the real world given the implications of their wave functions and the Heisenberg Uncertainty Principle. It explores theoretical models, approximations, and practical applications in physics.

Discussion Character

  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants suggest that the wave function of a free particle, represented as A exp(ikx), implies that the particle can be found everywhere, raising the question of whether free particles exist in reality.
  • Others argue that while the mathematical representation suggests infinite spatial probability, practical considerations, such as the size of particles relative to their environments, allow for the approximation of "free" particles in certain contexts, like conduction electrons in metals.
  • A later reply clarifies that a true free particle with a completely definite momentum (Δp = 0) does not exist in reality, as realistic wave functions must be wave packets with finite momentum spread (Δp), leading to finite spatial localization (Δx) due to the Heisenberg Uncertainty Principle.
  • One participant emphasizes that making appropriate approximations is a fundamental aspect of doing physics, highlighting the utility of the plane wave wave function in various scenarios.

Areas of Agreement / Disagreement

Participants express differing views on the existence of free particles, with some supporting the idea that approximations allow for practical applications while others emphasize the limitations imposed by quantum mechanics. The discussion remains unresolved regarding the existence of true free particles.

Contextual Notes

Limitations include the dependence on definitions of "free particle" and the implications of wave functions in quantum mechanics. The discussion also highlights the role of approximations in practical physics applications.

matness
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maybe it is an easy question but i confuse a bit


wave func of free particle is A exp(ikx) and probability over all space is
A^2 so it is possible to find this particle everywhere


Does it mean "there exist no free particle in real world" ?
 
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matness said:
maybe it is an easy question but i confuse a bit


wave func of free particle is A exp(ikx) and probability over all space is
A^2 so it is possible to find this particle everywhere


Does it mean "there exist no free particle in real world" ?

At some point, you have to consider what is "small enough" to no longer be significant, and what is "large enough" to consider it to be edgeless.

On paper, the influence of the gravity from Alpha Centauri is not zero. But it would look silly if all our dynamical description would have to include such things. The same thing with "free electron". Compare to its "size", such as its deBroglie wavelength, there are MANY situation in which the electron has no clue that it has a boundary. In a typical metal, the conduction electron in your tiny wires can be considered as "free" electrons. This is because using such an approximation (called the Drude model), we could obtain practically all the usual properties of a conductor, such as Ohm's Law. When it works this well, it is very difficult to argue that such an assumption is incorrect.

Other situations such as in particle accelerators explicitly considers charged particles/electrons to be free.

Zz.
 
matness said:
wave func of free particle

...with a completely definite value of momentum [itex]p[/itex], that is, [itex]\Delta p = 0[/itex]...

is A exp(ikx)

...where [itex]k = p / \hbar[/itex]...

and probability over all space is A^2 so it is possible to find this particle everywhere

...that is, [itex]\Delta x = \infty[/itex].


Does it mean "there exist no free particle in real world" ?

No, it means, "there exist no free particle with [itex]\Delta p = 0[/itex] in the real world." A realistic wave function for a free particle is a wave packet: a superposition of waves with a finite spread [itex]\Delta p[/itex] in momentum, which leads to a finite spatial width [itex]\Delta x[/itex] according to Heisenberg's Uncertainty Principle.
 
Doing physics means making appropriate approximations.
The plane wave WF is very useful for many of these.
 

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