In physics, coupling is when two objects are interacting with each other, that is they are not independent. In classical mechanics, coupling is a connection between two oscillating systems, such as pendulums connected by a spring. The connection affects the oscillatory pattern of both objects. In particle physics, <dfn>two particles are coupled </dfn>if they are connected by <dfn>one of the four </dfn>fundamental forces.
Wave mechanics
Coupled harmonic oscillator
thumb|Coupled pendulums connected by a spring
If two waves are able to transmit energy to each other, then these waves are said to be "coupled." This normally occurs when the waves share a common component. An example of this is two pendulums connected by a spring. If the pendulums are identical, then their equations of motion are given by
<math display="block">m\ddot{x} = -mg\frac{x}{l_1} - k(x-y)</math>
<math display="block">m\ddot{y} = -mg \frac{y}{l_2} + k(x-y)</math>
These equations represent the simple harmonic motion of the pendulum with an added coupling factor of the spring. This behavior is also seen in certain molecules (such as CO<sub>2</sub> and H<sub>2</sub>O), wherein two of the atoms will vibrate around a central one in a similar manner.
Astrophysics
Objects in space which are coupled to each other are under the mutual influence of each other's gravity. For instance, the Earth is coupled to both the Sun and the Moon, as it is under the gravitational influence of both. Common in space are binary systems, two objects gravitationally coupled to each other. Examples of this are binary stars which circle each other. Multiple objects may also be coupled to each other simultaneously, such as with globular clusters and galaxy groups. When smaller particles, such as dust, which are coupled together over time accumulate into much larger objects, accretion is occurring. This is the major process by which stars and planets form.
Plasma
The coupling constant of a plasma is given by the ratio of its average Coulomb-interaction energy to its average kinetic energy—or how strongly the electric force of each atom holds the plasma together. Plasmas can therefore be categorized into weakly- and strongly-coupled plasmas depending upon the value of this ratio. Many of the typical classical plasmas, such as the plasma in the solar corona, are weakly coupled, while the plasma in a white dwarf star is an example of a strongly coupled plasma. If the two systems have similar total energy, then the system may undergo Rabi oscillation. For example, two electrons orbiting around the same nucleus may have coupled angular momenta. Due to the 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