The ionization rate is the total probability current through the outer classical turning point.
2.
Where " ? " is the probability density function corresponding to the time component, and "'j "'is the probability current vector.
3.
In non-relativistic quantum mechanics, the probability current "'j "'of the wave function " ? " in one dimension is defined as
4.
Instead, what appears look at first sight a " probability density " and " probability current " has to be reinterpreted as charge density and current density when multiplied by electric charge.
5.
The definition of probability current and Schr�dinger's equation can be used to derive the continuity equation, which has " exactly " the same forms as those for hydrodynamics and electromagnetism:
6.
Where " j " inc, " j " ref and " j " trans are the incident, reflected and transmitted probability currents respectively, and the vertical bars indicate the magnitudes of the current vectors.
7.
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.
8.
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.
9.
In RQM, while is a wavefunction, the probability interpretation is not the same as in non-relativistic QM . Some RWEs do not predict a probability density or probability current ( really meaning " probability current density " ) because they are " not " positive definite functions of space and time.
10.
In RQM, while is a wavefunction, the probability interpretation is not the same as in non-relativistic QM . Some RWEs do not predict a probability density or probability current ( really meaning " probability current density " ) because they are " not " positive definite functions of space and time.
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