Charge Density (quantum Mechanics)
In quantum mechanics, charge density ρq is related to wavefunction ψ(r) by the equation
where q is the charge of the particle and |ψ(r)|2 = ψ*(r)ψ(r) is the probability density function i.e. probability per unit volume of a particle located at r.
When the wavefunction is normalized - the average charge in the region r ∈ R is
where d3r is the integration measure over 3d position space.
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—William Shakespeare (1564–1616)