Probability and probability current densities in one dimension
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A probability density, however, measures probability over a unit of space (or time, or phase space, or whatever), and thus its unit is the inverse of the unit you're using to measure the space the density is distributed over.
For example, if you have a probability density over a one-dimensional space measured in meters, then the unit of the probability density is 1 / meter. If the probability density was distributed over a two-dimensional space, you'd measure it in units of 1 / meter², and if it was a density over time, you could measure it in units of 1 / second, etc.
Similarly, a probability current is a measure of the probability (which, again, is dimensionless) passing through the boundary of an area per unit of time. Thus, if the boundary is measured in units of X, the probability current is measured in units of 1 / X / second (or whichever unit of time you're using). Of course, in one-dimensional space, a boundary is simply a point, and thus also dimensionless, so the probability flux in 1D space simply has units of 1 / second.
hope it helps
For example, if you have a probability density over a one-dimensional space measured in meters, then the unit of the probability density is 1 / meter. If the probability density was distributed over a two-dimensional space, you'd measure it in units of 1 / meter², and if it was a density over time, you could measure it in units of 1 / second, etc.
Similarly, a probability current is a measure of the probability (which, again, is dimensionless) passing through the boundary of an area per unit of time. Thus, if the boundary is measured in units of X, the probability current is measured in units of 1 / X / second (or whichever unit of time you're using). Of course, in one-dimensional space, a boundary is simply a point, and thus also dimensionless, so the probability flux in 1D space simply has units of 1 / second.
hope it helps
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