Editing Field equation (section)

===Origin===

Usually, field equations are postulated (like the [[Einstein field equations]] and the [[Schrödinger equation]], which underlies all quantum field equations) or obtained from the results of experiments (like [[Maxwell's equations]]). The extent of their validity is their ability to correctly predict and agree with experimental results.

From a theoretical viewpoint, field equations can be formulated in the frameworks of [[Lagrangian field theory]], [[Hamiltonian field theory]], and field theoretic formulations of the [[principle of stationary action]].<ref>{{cite book |last1=Goldstein |first1=Herbert |author-link1=Herbert Goldstein | title=Classical Mechanics |url=https://archive.org/details/classicalmechani00gold_639 |url-access=limited |edition=2nd |year=1980|isbn= 0201029189|publisher=Addison Wesley |chapter=Chapter 12: Continuous Systems and Fields|location=San Francisco, CA |pages=[https://archive.org/details/classicalmechani00gold_639/page/n565 548], 562}}</ref> Given a suitable Lagrangian or Hamiltonian density, a function of the fields in a given system, as well as their derivatives, the principle of stationary action will obtain the field equation.