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Meaning of zero probability density

by xfshi2000
Tags: density, meaning, probability
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xfshi2000
#1
Feb13-09, 09:40 AM
P: 31
Hi
I have a question about zero point of probability density of particle. In general we say if probability density is zero at a certain position, the particle never arrive there. But I also read some post in this forum. They said zero probability density means you have zero chance of seeing the particle. It doesn't mean the particle never arrive there. Only because of wave function interference, we have zero chance to see them. For example, oscillator excited state, there are several nodes in the wave function. In real world, it still pass through the zero probability density position. Where I use inaccurate word, there is no accurate position measurement. Another example is double slit experiment. We see alternate bright band and dark band in the screen. Dark band means that we cannot see the photon reach those places but photon really visit there. Because of interference of wave function, we have no chance to see them. Is my understanding right? if wrong, where does I make a mistake? thanks
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JosephButler
#2
Feb13-09, 09:48 AM
P: 18
Hi xfshi, in quantum mechanics it's a bit ill-posed to ask if a particle ever `arrives' somewhere. The meaningful thing to ask is whether or not you observe the particle. Zero probability density indeed means zero chance of observing the particle in that state (e.g. at that position).

It is less meaningful to ask whether the particle actually "does" pass through that point. The probability density doesn't say anything about how a particle got to the position you're observing; e.g. it doesn't tell you if a particle passes through a given point unobserved en route to being observed elsewhere.

This is one of the weird and cute features of quantum physics.
xfshi2000
#3
Feb13-09, 04:33 PM
P: 31
Quote Quote by JosephButler View Post
Hi xfshi, in quantum mechanics it's a bit ill-posed to ask if a particle ever `arrives' somewhere. The meaningful thing to ask is whether or not you observe the particle. Zero probability density indeed means zero chance of observing the particle in that state (e.g. at that position).

It is less meaningful to ask whether the particle actually "does" pass through that point. The probability density doesn't say anything about how a particle got to the position you're observing; e.g. it doesn't tell you if a particle passes through a given point unobserved en route to being observed elsewhere.

This is one of the weird and cute features of quantum physics.
Thank you for your reply. I agree with you. As I know there are infinite paths for particle from one position to another position(path integral). Classical path is the one with maximum probability. We indeed have no chance to observe it at zero probability density at a node point. But we don't know whether or not it pass through that specific point. thanks again.


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