About probability densities

  • Thread starter churi55
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It is well known that the wave function for a free particle in a one-dimentional 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-dimentional 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 continous thereafter.
 

dextercioby

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The wavefunction's incorrectly written.Notice that the only relevant physical quantity is the probability.

Daniel.
 
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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?
 

Chronos

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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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