Charge Density - Charge Density (quantum Mechanics)

Charge Density (quantum Mechanics)

In quantum mechanics, charge density ρ_q 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.