Editing Momentum (section)

===Quantum mechanical===
{{Further|Momentum operator}}
In [[quantum mechanics]], momentum is defined as a [[self-adjoint operator]] on the [[wave function]]. The [[Werner Heisenberg|Heisenberg]] [[uncertainty principle]] defines limits on how accurately the momentum and position of a single observable system can be known at once. In quantum mechanics, position and momentum are [[conjugate variables]].

For a single particle described in the position basis the momentum operator can be written as

<math display="block">\mathbf{p}={\hbar\over i}\nabla=-i\hbar\nabla\,,</math>

where {{math|∇}} is the [[gradient]] operator, {{mvar|ħ}} is the [[reduced Planck constant]], and {{mvar|i}} is the [[imaginary unit]]. This is a commonly encountered form of the momentum operator, though the momentum operator in other bases can take other forms. For example, in [[momentum space]] the momentum operator is represented by the [[eigenvalue]] equation

<math display="block">\mathbf{p}\psi(p) = p\psi(p)\,,</math>

where the operator {{math|'''p'''}} acting on a wave eigenfunction {{math|{{var|ψ}}({{var|p}})}} yields that wave function multiplied by the eigenvalue {{mvar|p}}, in an analogous fashion to the way that the position operator acting on a wave function {{math|{{var|ψ}}({{var|x}})}} yields that wave function multiplied by the eigenvalue {{mvar|x}}.

For both massive and massless objects, relativistic momentum is related to the [[phase constant]] {{mvar|β}} by<ref>{{cite journal |first=Z. Y. |last=Wang |title=Generalized momentum equation of quantum mechanics |journal=Optical and Quantum Electronics |volume=48 |date=2016 |doi=10.1007/s11082-015-0261-8 |issue=2 |page=107 |bibcode=2016OQEle..48..107W |s2cid=124732329}}</ref>

<math display="block"> p = \hbar \beta</math>

[[Electromagnetic radiation]] (including [[light|visible light]], [[ultraviolet]] light, and [[radio waves]]) is carried by [[photons]]. Even though photons (the particle aspect of light) have no mass, they still carry momentum. This leads to applications such as the [[solar sail]]. The calculation of the momentum of light within [[dielectric]] media is somewhat controversial (see [[Abraham–Minkowski controversy]]).<ref>{{cite journal |last=Barnett |first=Stephen M. |title=Resolution of the Abraham-Minkowski Dilemma |journal=Physical Review Letters |date=2010 |volume=104 |issue=7 |page=070401 |doi=10.1103/PhysRevLett.104.070401 |bibcode = 2010PhRvL.104g0401B |pmid=20366861 |url=https://strathprints.strath.ac.uk/26871/5/AbMinPRL.pdf}}</ref><ref>{{cite journal
 |author1=Wang Zhong-Yue |author2=Wang Pin-Yu |author3=Xu Yan-Rong | date=2011 | title=Crucial experiment to resolve Abraham-Minkowski Controversy | journal=Optik | volume=122 | pages=1994–1996 | doi=10.1016/j.ijleo.2010.12.018 | issue= 22|bibcode = 2011Optik.122.1994W |arxiv=1103.3559 |s2cid=119209160 }}</ref>