Editing Probability amplitude (section)

{{short description|Complex number whose squared absolute value is a probability}}
{{About|probability amplitude in quantum mechanics|other uses|Amplitude (disambiguation)}}
{{more citations needed|date=January 2014}}
[[File:Hydrogen eigenstate n5 l2 m1.png|thumb|
A [[wave function]] for a single [[electron]] on 5d [[atomic orbital]] of a [[hydrogen atom]]. The solid body shows the places where the electron's [[probability density function|probability density]] is above a certain value (here 0.02 [[nanometre|nm]]<sup>−3</sup>): this is calculated from the probability amplitude. The [[hue]] on the colored surface shows the [[argument (complex analysis)|complex phase]] of the wave function.]]
In [[quantum mechanics]], a '''probability amplitude''' is a [[complex number]] used for describing the behaviour of systems. The square of the [[Absolute value|modulus]] of this quantity at a point in space represents a [[probability density function|probability density]] at that point.

Probability amplitudes provide a relationship between the [[quantum state]] vector of a system and the results of observations of that system, a link that was first proposed by [[Max Born]], in 1926. Interpretation of values of a wave function as the probability amplitude is a pillar of the [[Copenhagen interpretation]] of quantum mechanics. In fact, the properties of the space of wave functions were being used to make physical predictions (such as [[atomic emission spectroscopy|emissions from atoms]] being at certain discrete energies) before any physical interpretation of a particular function was offered. Born was awarded half of the 1954 [[Nobel Prize in Physics]] for this understanding, and the probability thus calculated is sometimes called the "Born probability". These probabilistic concepts, namely the probability density and [[quantum measurement]]s, were vigorously contested at the time by the original physicists working on the theory, such as [[Erwin Schrödinger|Schrödinger]] and [[Albert Einstein|Einstein]]. It is the source of the mysterious consequences and philosophical difficulties in the [[interpretations of quantum mechanics]]—topics that continue to be debated even today.