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If the [itex]|\psi|^2[/itex] is defined for a 3 dimensional system, then the probability density will be the probability divided by volume. And for 2 dimensional and 1 dimensional systems, we have area and length respectively.

The best way to see this is that for 1 dimensional systems, for example, the probability of a particle being between points A and B is given by

[tex]\int^B_A |\psi(x)|^2\ dx.[/tex]

Here, we have multiplied the prob. density by a length, namely [itex]dx,[/itex] to get a probability. Therefore the density itself is a probability divided by a length. The extension to higher dimensions is easy.

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mathman

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Hurkyl

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Probability densityPlease correct me if this is wrong. SO what exactly does the "density" refer to?

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Nope, that's incorrect. It's the probability ascribed to a finite/infinite domain (in any # of dimensions, 1,2,3,...), not to a point of the domain.at a certain positionat a certain time. Please correct me if this is wrong. SO what exactly does the "density" refer to?

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NOW, I think understand why they call it probability

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