How Can a Particle Transition Between Sides in an Infinite Potential Well?

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Discussion Overview

The discussion revolves around the behavior of a particle in an infinite potential well, particularly addressing the implications of the wave function and probability density on the particle's ability to transition between sides of the well. The conversation also touches on concepts related to quantum uncertainty and cosmological observations.

Discussion Character

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

Main Points Raised

  • Some participants assert that the wave function for a particle in an infinite potential well is sinusoidal, with nodes at the boundaries, leading to equal probabilities of finding the particle on either side of the well.
  • Others argue that the particle does not actually move in the classical sense and that the probability density must be integrated over a region to determine the likelihood of finding the particle there.
  • A participant suggests that the zero probability density at the midpoint does not prevent the particle from being described as a wave, where amplitude can be zero at a point but still continuous elsewhere.
  • One participant points out a potential error in the wave function representation, emphasizing that the relevant physical quantity is probability.
  • A thought experiment is introduced regarding the implications of the uncertainty principle in the context of astronomical observations and the expansion of the universe, questioning if this could explain spontaneous particle generation in intergalactic space.
  • Another participant states that the uncertainty principle does not apply at macroscopic scales, prompting further clarification from others regarding the measurement of momentum and position.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the interpretation of the wave function and the implications of the uncertainty principle, indicating that the discussion remains unresolved.

Contextual Notes

There are limitations in the assumptions made about the wave function and the implications of the uncertainty principle, particularly in relation to macroscopic versus quantum scales. The discussion also reflects varying interpretations of probability and measurement in quantum mechanics.

churi55
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It is well known that the wave function for a free particle in a one-dimensional infinite potential well is just a sinusodial wave with each end being a node.

Let me suppose that the infinite square well is v=infinity at x=0,L and the coresponding wave function is sqrt(2/L)*sin(2*Pi/L).

From the wave function, the probability of finding the particle on the left side (x=0~L/2) and the right side (x=L/2~L) are exactly the same.

The question is, if at x=L/2 (midpoint) the probability density is 0, how can the particle go from the left to the right?
 
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Firstly the particle doesn't actually move; to see it moving you put it into a position eigenstate, and furthermore, you want to integrate the probability density function from one value of x to another to get the probability of the particle being in that region.
 
churi55 said:
It is well known that the wave function for a free particle in a one-dimensional infinite potential well is just a sinusodial wave with each end being a node.

Let me suppose that the infinite square well is v=infinity at x=0,L and the coresponding wave function is sqrt(2/L)*sin(2*Pi/L).

From the wave function, the probability of finding the particle on the left side (x=0~L/2) and the right side (x=L/2~L) are exactly the same.

The question is, if at x=L/2 (midpoint) the probability density is 0, how can the particle go from the left to the right?

Maybe you can put the 'particle' like picture away for a minute and think of it in terms of wave. Then amplitude of wave could be zero at one point but follows continuous thereafter.
 
The wavefunction's incorrectly written.Notice that the only relevant physical quantity is the probability.

Daniel.
 
Quantim uncertianty and spontainous particle generation

Here is an interesting thought experiment.
An astronomical observation of the redshift of very distant objects reveals that their velocity approaches the speed of light. If Hubbels interpretation is correct regarding the expanding universe the implication is that there is a relativistic horizon where Vr (Velocity of recession) is equal to c. Nothing can be observed beyond this distance and it is probably meaningless to refer to anything "outside" this horizon.
Now here is the question. Given the uncertianty principal the more accurately we know the momentum of an object the less accurately we know its location. If we "know" the recession velocity of an object to be vanishingly close to c then we know "nothing about its location." The object, once observed, can be anywhere in the universe! Could this explain the apearant spontanious production of particles in intergalactic space? If so could this be an alternative explanation to the expansion of the universe?
 
HUP does not apply at macroscopic scales.
 
Following from dextercioby's comments, consider a helical wavefunction...
 
ProfChuck said:
Here is an interesting thought experiment.
An astronomical observation of the redshift of very distant objects reveals that their velocity approaches the speed of light. If Hubbels interpretation is correct regarding the expanding universe the implication is that there is a relativistic horizon where Vr (Velocity of recession) is equal to c. Nothing can be observed beyond this distance and it is probably meaningless to refer to anything "outside" this horizon.
Now here is the question. Given the uncertianty principal the more accurately we know the momentum of an object the less accurately we know its location. If we "know" the recession velocity of an object to be vanishingly close to c then we know "nothing about its location." The object, once observed, can be anywhere in the universe! Could this explain the apearant spontanious production of particles in intergalactic space? If so could this be an alternative explanation to the expansion of the universe?

Try to think on what you really measure in order to avoid such wrong deductions from the HUP.

HUP allows you to know with a fantastic precision (with a 0 error at the limit) some values, such as the position and velocity of macroscopic objects.


Chronos said:
HUP does not apply at macroscopic scales.

What do you mean?

Seratend.
 
seratend said:
What do you mean?

It looks like he was referring to ProfChuck just to say that our ability to measure momentum of a macroscopic object is so inexact that it removes the possibility of a significant HUP effect.
 

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