Editing Electron density (section)

{{Short description|Probability density of electrons being somewhere}}
{{About|the quantum mechanical probability density of an electron|the number density of electrons in a plasma, also called "electron density"|Plasma (physics)}}
{{Use British English|date = August 2021}}

'''Electron density''' or '''electronic density''' is the measure of the [[probability]] of an [[electron]] being present at an infinitesimal element of space surrounding any given point. It is a scalar quantity depending upon three spatial variables and is typically denoted as either <math>\rho(\textbf r)</math> or <math>n(\textbf r)</math>. The density is determined, through definition, by the normalised <math>N</math>-electron [[wavefunction]] which itself depends upon <math>4N</math> variables (<math display="inline">3N</math> spatial and <math>N</math> [[Spin (physics)|spin]] coordinates). Conversely, the density determines the wave function modulo up to a phase factor, providing the formal foundation of [[density functional theory]].

According to [[quantum mechanics]], due to the [[uncertainty principle]] on an atomic scale the exact location of an electron cannot be predicted, only the probability of its being at a given position; therefore electrons in atoms and molecules act as if they are "smeared out" in space. For one-electron systems, the electron density at any point is proportional to the square magnitude of the wavefunction.