Editing Electron (section)

=== Quantum properties ===
As with all particles, electrons can act as waves. This is called the [[wave–particle duality]] and can be demonstrated using the [[double-slit experiment]].

The wave-like nature of the electron allows it to pass through two parallel slits simultaneously, rather than just one slit as would be the case for a classical particle. In quantum mechanics, the wave-like property of one particle can be described mathematically as a [[complex number|complex]]-valued function, the [[wave function]], commonly denoted by the [[Greek alphabet|Greek letter]] [[Psi (Greek)|psi]] (''ψ''). When the [[Absolute value#Complex numbers|absolute value]] of this function is [[square (algebra)|squared]], it gives the probability that a particle will be observed near a location—a [[probability density function|probability density]].<ref name="munowitz">
{{cite book
 | last = Munowitz | first = M.
 | year = 2005
 | title = Knowing the Nature of Physical Law
 | url = https://archive.org/details/knowingnatureofp0000muno
 | url-access = registration | page = [https://archive.org/details/knowingnatureofp0000muno/page/162 162] | publisher = Oxford University Press
 | isbn = 978-0-19-516737-5
}}</ref>{{rp|162–218}}

[[File:Asymmetricwave2.png|right|thumb|alt=A three dimensional projection of a two dimensional plot. There are symmetric hills along one axis and symmetric valleys along the other, roughly giving a saddle-shape|Example of an antisymmetric wave function for a quantum state of [[Particle in a box|two identical fermions in a one-dimensional box]], with each horizontal axis corresponding to the position of one particle. If the particles swap position, the wave function inverts its sign.]]
Electrons are [[identical particles]] because they cannot be distinguished from each other by their intrinsic physical properties. In quantum mechanics, this means that a pair of interacting electrons must be able to swap positions without an observable change to the state of the system. The wave function of fermions, including electrons, is antisymmetric, meaning that it changes sign when two electrons are swapped; that is, {{nowrap|''ψ''(''r''<sub>1</sub>, ''r''<sub>2</sub>) {{=}} −''ψ''(''r''<sub>2</sub>, ''r''<sub>1</sub>)}}, where the variables ''r''<sub>1</sub> and ''r''<sub>2</sub> correspond to the first and second electrons, respectively. Since the absolute value is not changed by a sign swap, this corresponds to equal probabilities. [[Boson]]s, such as the photon, have symmetric wave functions instead.<ref name="munowitz" />{{rp|162–218}}

In the case of antisymmetry, solutions of the wave equation for interacting electrons result in a [[zero probability]] that each pair will occupy the same location or state. This is responsible for the [[Pauli exclusion principle]], which precludes any two electrons from occupying the same quantum state. This principle explains many of the properties of electrons. For example, it causes groups of bound electrons to occupy different [[atomic orbital|orbitals]] in an atom, rather than all overlapping each other in the same orbit.<ref name="munowitz" />{{rp|162–218}}