probability current

The ionization rate is the total probability current through the outer classical turning point.

The definition of the probability current associated with the Dirac equation is:

Such a bidirectional-arrow notation is frequently used for describing the probability current of quantum mechanics.

In physical terms, this represents an electrical current of Maxwell's electromagnetic theory, or more generally a probability current.

The chance of finding the particle at some position r and time t flows like a fluid; hence the term probability current, a vector field.

The notion of a probability current is useful in some of the formalism in quantum mechanics.

Having the metaphor of probability density as mass density, then probability current is the current:

The probability current (aka probability flux):

Intuitively; if one pictures the probability density as an inhomogeneous fluid, then the probability current is the rate of flow of this fluid.

In regions where a step potential or potential barrier occurs, the probability current is related to the transmission and reflection coefficients, respectively T and R; they measure the extent the particles reflect from the potential barrier or are transmitted through it.

Other observables would not lead to that conclusion, but there need not be any problem in defining a mathematical theory for other observables; see Hyman et al. for an exploration of the fact that a probability density and probability current can be defined for any set of commuting operators.