Coupling (physics)
Coupling in science |
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Classical coupling |
Quantum coupling |
In physics, two objects are said to be coupled when they are interacting with each other. 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, two particles are coupled if they are connected by one of the four fundamental forces.
Wave mechanics
Coupled harmonic oscillator
If two
These equations represent the simple harmonic motion of the pendulum with an added coupling factor of the spring.[1] This behavior is also seen in certain molecules (such as CO2 and H2O), wherein two of the atoms will vibrate around a central one in a similar manner.[1]
Coupled LC circuits
In LC circuits, charge oscillates between the capacitor and the inductor and can therefore be modeled as a simple harmonic oscillator. When the magnetic flux from one inductor is able to affect the inductance of an inductor in an unconnected LC circuit, the circuits are said to be coupled.[1] The coefficient of coupling k defines how closely the two circuits are coupled and is given by the equation
where M is the
Chemistry
Spin-spin coupling
Spin-spin coupling occurs when the magnetic field of one atom affects the magnetic field of another nearby atom. This is very common in NMR imaging. If the atoms are not coupled, then there will be two individual peaks, known as a doublet, representing the individual atoms. If coupling is present, then there will be a triplet, one larger peak with two smaller ones to either side. This occurs due to the spins of the individual atoms oscillating in tandem.[2]
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.[3]
Plasma
The coupling constant of a
Quantum mechanics
Two coupled quantum systems can be modeled by a Hamiltonian of the form
Angular momentum coupling
When
Particle physics and quantum field theory
Particles which interact with each other are said to be coupled. This interaction is caused by one of the fundamental forces, whose strengths are usually given by a dimensionless coupling constant. In quantum electrodynamics, this value is known as the fine-structure constant α, approximately equal to 1/137. For quantum chromodynamics, the constant changes with respect to the distance between the particles. This phenomenon is known as asymptotic freedom. Forces which have a coupling constant greater than 1 are said to be "strongly coupled" while those with constants less than 1 are said to be "weakly coupled."[7]
References
- ^ ISBN 0-471-93742-8.
- ^ "5.5 Spin-Spin Coupling". Chemistry Libretexts. 2015-07-21. Retrieved 13 Apr 2017.
- ISBN 978-0-7167-1927-4.
- ^ ISBN 978-0-8053-8754-4.
- ^ ISBN 978-0-471-20276-9.
- ^ ISBN 978-0-471--88702-7.
- ISBN 978-3-527-40601-2.