Quantum Mechanics: Understanding Probability and Current Flow

AI Thread Summary
The discussion revolves around the interpretation of quantum current density and its relationship to the wave function in quantum mechanics. The user is confused about how the wave function leads to a current density (j) of 1, questioning if this implies that one particle passes through a unit area each second. They express concern that substituting the wave function directly into the equation seems overly simplistic and may overlook important details. The user references external sources, including Wikipedia, to clarify that j represents the number of particles passing through a unit area per unit time, but they are still puzzled by the cancellation of units. This highlights a need for deeper understanding of how quantum mechanics quantifies particle flow.
physicsjock
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quantum current question

Hey,

I've been trying to work out this question and I'm really struggling to work out what to do.

http://img36.imageshack.us/img36/9759/afasp.jpg

I know that the units of current density is flow per unit area but I can't see a way to use that to prove the wave function has units such that exactly one particle passes per second.

When I sub the wave function into j I get j=1, all the units and everything cancel out.

Does getting j=1 mean only 1 particle flows through a unit area each second?

Substituting the wave function straight in seems too simple to answer the question,

Is there something I have missed?

Thanks in advanced
 
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I've been looking around and reading around,

I found this, haha off wiki, it's consistent with some lecture slides I found online aswell.

http://en.wikipedia.org/wiki/Flux#Quantum_mechanics

"Then the number of particles passing through a perpendicular unit of area per unit time is J"

The thing that has me stumped is that its supposed to be flux right? Why do all the units cancel out? Is J just supposed to represent the NUMBER of particles?
 
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