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632:—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
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are the inductances of the primary and secondary circuits, respectively. If the flux lines of the primary inductor thread every line of the secondary one, then the coefficient of coupling is 1 and
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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
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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
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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."
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980:. As they are both forms of angular momentum, they must be conserved. Even if energy is transferred between the two, the total angular momentum,
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586:. 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
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of an inductor in an unconnected LC circuit, the circuits are said to be coupled. The coefficient of coupling k defines how closely the
412:
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968:(also known as spin-orbit coupling) is a special case of angular momentum coupling. Specifically, it is the interaction between the
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649:
987:
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of the pendulum with an added coupling factor of the spring. This behavior is also seen in certain molecules (such as
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which is the addition of the two
Hamiltonians in isolation with an added interaction factor. In most simple systems,
559:
602:. When smaller particles, such as dust, which are coupled together over time accumulate into much larger objects,
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which circle each other. Multiple objects may also be coupled to each other simultaneously, such as with
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1057:, the constant changes with respect to the distance between the particles. This phenomenon is known as
913:, the total angular momentum is always the sum of the individual angular momenta of the electrons, or
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from two separate sources interact with each other, they are said to be coupled. For example, two
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Objects in space which are coupled to each other are under the mutual influence of each other's
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connected by a spring. The connection affects the oscillatory pattern of both objects. In
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Dispersion relations for non-coupled, weakly-coupled, and strongly-coupled particles
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O), wherein two of the atoms will vibrate around a central one in a similar manner.
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185:. If the pendulums are identical, then their equations of motion are given by
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875:. If the two systems have similar total energy, then the system may undergo
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590:, two objects gravitationally coupled to each other. Examples of this are
1038:
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is occurring. This is the major process by which stars and planets form.
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134:
753:{\displaystyle {\hat {H}}={\hat {H}}_{a}+{\hat {H}}_{b}+{\hat {V}}_{ab}}
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and can therefore be modeled as a simple harmonic oscillator. When the
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1174:. Menlo Park, California: Benjamin/Cumming Publishing Company.
16:
Two systems are coupled if they are interacting with each other
958:{\displaystyle \mathbf {J} =\mathbf {J_{1}} +\mathbf {J_{2}} }
558:
magnetic field of another nearby atom. This is very common in
1198:
Hagelstein, Peter; Senturia, Stephen; Orlando, Terry (2004).
125:
to be coupled when they are interacting with each other. In
341:{\displaystyle m{\ddot {y}}=-mg{\frac {y}{l_{2}}}+k(x-y)}
260:{\displaystyle m{\ddot {x}}=-mg{\frac {x}{l_{1}}}-k(x-y)}
1200:
Introductory
Applied Quantum and Statistical Mechanics
1015:{\displaystyle \mathbf {J} =\mathbf {L} +\mathbf {S} }
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562:. If the atoms are not coupled, then there will be
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453:
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259:
640:star is an example of a strongly coupled plasma.
454:{\displaystyle {\frac {M}{\sqrt {L_{p}L_{s}}}}=k}
1091:(Fourth ed.). West Sussex, England: Wiley.
648:Two coupled quantum systems can be modeled by a
574:of the individual atoms oscillating in tandem.
905:may have coupled angular momenta. Due to the
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8:
636:, are weakly coupled, while the plasma in a
526:, so most systems are not perfectly coupled.
1255:Elementary Particle-Second, Revised Edition
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1026:Particle physics and quantum field theory
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533:Peaks in an NMR image of Ethyl Acetate.
169:Coupled pendulums connected by a spring
129:, coupling is a connection between two
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1053:α, approximately equal to 1/137. For
624:is given by the ratio of its average
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976:, and its orbital angular momentum,
570:either side. This occurs due to the
1089:The Physics of Vibrations and Waves
616:Frequency classification of plasmas
515:{\textstyle M={\sqrt {L_{p}L_{s}}}}
984:, of the system must be constant,
14:
522:In practice, however, there is of
377:Two LC circuits coupled together.
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1000:
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945:
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907:conservation of angular momentum
385:, charge oscillates between the
864:{\displaystyle {\hat {V}}_{ab}}
37:Rotational–vibrational coupling
1202:. Hoboken, New Jersey: Wiley.
846:
825:{\displaystyle {\hat {H}}_{b}}
810:
789:{\displaystyle {\hat {H}}_{a}}
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350:These equations represent the
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1:
1049:, this value is known as the
409:and is given by the equation
1146:. W.H. Freeman and Company.
832:can be solved exactly while
1228:Merzbacher, Eugene (1998).
620:The coupling constant of a
161:Coupled harmonic oscillator
55:Ro–vibrational spectroscopy
1305:
1138:Kaufmann, William (1988).
1034:Examples of gluon coupling
886:
613:
143:two particles are coupled
1253:Griffiths, David (2010).
1232:(Third ed.). Wiley.
1170:Ichimaru, Setsuo (1986).
911:angular momentum operator
901:orbiting around the same
889:Angular momentum coupling
883:Angular momentum coupling
145:if they are connected by
70:Angular momentum coupling
1142:Universe, Second Edition
1113:"5.5 Spin-Spin Coupling"
407:two circuits are coupled
1051:fine-structure constant
1047:quantum electrodynamics
1055:quantum chromodynamics
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1016:
966:Spin-Orbit interaction
959:
909:and the nature of the
871:can be solved through
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628:energy to its average
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467:of the circuits and L
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399:one inductor is able
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177:are able to transmit
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123:two objects are said
1117:Chemistry Libretexts
988:
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564:two individual peaks
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1087:Pain, H.J. (1993).
873:perturbation theory
626:Coulomb-interaction
369:Coupled LC circuits
127:classical mechanics
65:Rovibronic coupling
23:Coupling in science
1239:978-0-471--88702-7
1060:asymptotic freedom
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548:Spin-spin coupling
543:Spin-spin coupling
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150:fundamental forces
29:Classical coupling
1264:978-3-527-40601-2
1230:Quantum Mechanics
1209:978-0-471-20276-9
1181:978-0-8053-8754-4
1153:978-0-7167-1927-4
1043:coupling constant
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1121:. Retrieved
1119:. 2015-07-21
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634:solar corona
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592:binary stars
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578:Astrophysics
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380:
349:
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75:NMR coupling
22:
652:of the form
650:Hamiltonian
638:white dwarf
560:NMR imaging
524:ten leakage
383:LC circuits
131:oscillating
1278:Categories
1068:References
403:inductance
79:J-coupling
1039:Particles
899:electrons
847:^
811:^
775:^
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714:^
692:^
676:^
604:accretion
538:Chemistry
387:capacitor
330:−
292:−
283:¨
249:−
237:−
211:−
202:¨
135:pendulums
391:inductor
389:and the
903:nucleus
584:gravity
173:If two
119:physics
1261:
1236:
1206:
1178:
1150:
1123:13 Apr
1095:
622:plasma
610:Plasma
183:spring
179:energy
1284:Force
1045:. In
893:When
572:spins
471:and L
397:from
361:and H
175:waves
1259:ISBN
1234:ISBN
1204:ISBN
1176:ISBN
1148:ISBN
1125:2017
1093:ISBN
796:and
598:and
554:of
381:In
117:In
77:or
1280::
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1190:^
1162:^
1115:.
1075:^
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1184:.
1156:.
1127:.
1101:.
1062:.
1009:S
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1001:L
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993:J
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978:L
974:S
950:2
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935:1
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922:J
857:b
854:a
844:V
818:b
808:H
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772:H
746:b
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733:V
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711:H
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699:a
689:H
682:=
673:H
506:s
502:L
496:p
492:L
486:=
483:M
473:s
469:p
449:k
446:=
438:s
434:L
428:p
424:L
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363:2
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333:y
327:x
324:(
321:k
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311:2
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280:y
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252:y
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243:(
240:k
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214:m
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199:x
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
