Editing Coupling (physics) (section)

== Quantum mechanics ==
Two coupled quantum systems can be modeled by a [[Hamiltonian (quantum mechanics)|Hamiltonian]] of the form[[File:Spin orbit coupling dispersion relation.pdf|thumb|Dispersion relations for non-coupled, weakly-coupled, and strongly-coupled particles]]
<math display="block">\hat{H} = \hat{H}_a + \hat{H}_b + \hat{V}_{ab}</math>
which is the addition of the two Hamiltonians in isolation with an added interaction factor. In most simple systems, <math>\hat{H}_a</math> and <math>\hat{H}_b</math> can be solved exactly while <math>\hat{V}_{ab}</math> can be solved through [[Perturbation theory (quantum mechanics)|perturbation theory]].<ref name=":2">{{Cite book| title=Introductory Applied Quantum and Statistical Mechanics|last1=Hagelstein| first1=Peter| last2=Senturia|first2=Stephen| last3=Orlando|first3=Terry| publisher=Wiley |year=2004 |isbn=978-0-471-20276-9 |location=Hoboken, New Jersey}}</ref> If the two systems have similar total energy, then the system may undergo [[Rabi oscillation]].<ref name=":2" />

=== Angular momentum coupling ===
{{Main|Angular momentum coupling}}

When [[Angular momentum operator|angular momenta]] from two separate sources interact with each other, they are said to be coupled.<ref name=":3">{{Cite book| title=Quantum Mechanics | edition = Third |last=Merzbacher|first=Eugene |publisher=Wiley|year=1998 |isbn=978-0-471--88702-7}}</ref> For example, two [[electron]]s orbiting around the same [[Atomic nucleus|nucleus]] may have coupled angular momenta. Due to the [[Conservation of Angular Momentum|conservation of angular momentum]] and the nature of the [[angular momentum operator]], the total angular momentum is always the sum of the individual angular momenta of the electrons, or<ref name=":3" />
<math display="block">\mathbf{J}=\mathbf{J_1}+\mathbf{J_2}</math>
[[Spin–orbit interaction|Spin-Orbit interaction]] (also known as spin-orbit coupling) is a special case of angular momentum coupling. Specifically, it is the interaction between the [[Spin (physics)|intrinsic spin]] of a particle, '''S''', and its orbital angular momentum, '''L'''. As they are both forms of angular momentum, they must be conserved. Even if energy is transferred between the two, the total angular momentum, '''J''', of the system must be constant, <math>\mathbf{J}=\mathbf{L}+\mathbf{S}</math>.<ref name=":3" />