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Topic: Angular momentum coupling

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	Angular momentum - Wikipedia, the free encyclopedia
		In physics the angular momentum of an object with respect to a reference point is a measure for the extent to which, and the direction in which, the object rotates about the reference point.
		Angular momentum is important in physics because it is a conserved quantity: a system's angular momentum stays constant unless an external torque acts on it.
		Under this formalism, angular momentum is the 2-form Noether charge associated with rotational invariance (As a result, angular momentum isn't conserved for general curved spacetimes, unless it happens to be asymptotically rotationally invariant).
	en.wikipedia.org /wiki/Angular_momentum (1465 words)

	Angular momentum coupling - Wikipedia, the free encyclopedia
		The angular momentum coupling terms are the terms of the total Hamiltonian which do not commute with the subsystem individual angular momenta (or are not invariant with respect to the rotations of the subsystems).
		In Nuclear Magnetic Resonance spin-spin coupling is a kind of weak interaction between the spin of a nucleus and the spins of nearby nuclei.
		Spin-spin coupling or spin-spin splitting is the coupling of the spin angular momentum states of different particles.
	en.wikipedia.org /wiki/Angular_momentum_coupling (1322 words)

	Encyclopedia :: encyclopedia : Angular momentum (Site not responding. Last check: 2007-11-02)
		In particular, if the body rotates about an axis, then the angular momentum with respect to a point on the axis is related to the mass of the object, the angular velocity and the distance of the mass to the axis.
		Angular momentum can also be calculated by multiplying the square of the displacement 'r',the mass of the particle and the angular velocity.
		This implies that angular momentum is a conserved quantity as long as there is no net torque applied to the particle.
	www.hallencyclopedia.com /Angular_momentum (1013 words)

	Vector Model of Angular Momentum
		The orbital angular momentum for an atomic electron can be visualized in terms of a vector model where the angular momentum vector is seen as precessing about a direction in space.
		As in the case of the orbital angular momentum alone, the projection of the total angular momentum along a direction in space is quantized to values differeing by one unit of angular momentum.
		The z-component of angular momentum is quantized in values one unit apart, so for the upper level of the sodium doublet with j=3/2, the vector model gives the splitting shown.
	hyperphysics.phy-astr.gsu.edu /hbase/quantum/vecmod.html (565 words)

	Laser-assisted magnetic resonance : background
		Since angular momentum is a conserved quantity, the total angular momentum of the system (radiation and matter) cannot be changed during absorption and emission of radiation.
		Another possibility is the analysis of the fluorescence light: angular momentum conservation imposes correlations between the direction and polarization of the spontaneously emitted photons which depend on the angular momentum state of the excited atom.
		However, the different types of angular momentum are in general coupled to each other by various interactions which allow the polarization to flow from the photon spin reservoir through the electron orbital to all the other reservoirs, as shown schematically in figure 2.5.
	fuj.physik.uni-dortmund.de /~suter/lamr/background.html (3452 words)

	Drexel University Department of Physics (Site not responding. Last check: 2007-11-02)
		A similar diagonalization method is used to calculate the outer-product and inner-product coupling coefficients (isoscalar) factors of the permutation group [Chen,89].
		It reduces the I/O since the coupling coefficients and matrix elements of elementary operators only need to be stored in the individual subspaces (and not in a coupled form); for instance only 60 MB of input files are needed to perform calculations in the
		Each submatrix consists of the angular momentum states that belong to a given subshell symmetry.
	www.gothosenterprises.com /drexel/shell-code.html (613 words)

	Angular Momentum Coupling (Site not responding. Last check: 2007-11-02)
		This kind of combination is visualized in terms of a vector model of angular momentum.
		This kind of coupling is called L-S coupling or Russell-Saunders coupling, and it is found to give good agreement with the observed spectral details for many light atoms.
		In light atoms, the interactions between the orbital angular momenta of individual electrons is stronger than the spin-orbit coupling between the spin and orbital angular momenta.
	hyperphysics.phy-astr.gsu.edu /hbase/atomic/lcoup.html (257 words)

	CPC Licence Alert
		The accurate and fast calculation of the angular momentum coupling and recoupling coefficients is required in various branches of quantum many-particle physics.
		The presented code provides a fast and exact calculation of the angular momentum coupling and recoupling coefficients for large values of quantum angular momenta and is based on the GNU Library General Public License PLT software [1].
		A general angular momentum recoupling coefficient for an arbitrary number of (integer or half-integer) angular momenta is expressed as a sum over products of the Clebsch-Gordan coefficients.
	www.jinr.ru /programs/cpc_in18/summaries/ADWC.html (183 words)

	TCB Publications - Paper Request
		The angular momentum coefficients thus defined are general kinematic factors, depending only on the masses of the atoms and the product vibrational and translational distances, but not on the particular potential surface.
		Analytic formulas are derived for these angular momentum coefficients, both for reactions confined to a plane and for three-dimensional motion.
		An efficient and numerically stable method is derived for numerical evaluation of the angular momentum coefficients.
	www.ks.uiuc.edu /Publications/Papers/request.cgi?tbcode=SCHU76A (278 words)

	Angular Momentum Techniques in Quantum Mechanics (Fundamental Theories of Physics) by V. Devanathan [ISBN: 079235866X] ...
		This book deals with the coupling of two or more angular momenta, angular momentum coupling coefficients, rotation matrices, tensor operators, evaluation of matrix elements, the gradient formula, identical particles, statistical tensors and polarization phenomena, traces of angular momentum matrices, the helicity formalism and the spin states of the Dirac particle.
		These topics cover the entire range of angular momentum techniques that are being widely used in the study of both non-relativistic and relativistic problems in physics.
		It is also recommended as a text in angular momentum techniques for graduate students of physics and chemistry.
	www.gettextbooks.com /isbn_079235866X.html (178 words)

	Physics and Astronomy Department - Course Outline 1998
		First, the application of quantum mechanics to the case of angular momentum is illustrated.
		Angular momentum: classical definition, quantum mechanical treatment, commutation rules.
		General treatment of angular momentum: orbital and intrinsic angular momentum, matrix representations, description in terms of l,m, spin, addition of angular momentum, LS coupling scheme.
	www.le.ac.uk /physics/teach/recruit/year3/opt3646.htm (188 words)

	Angular(1)
		Conservation of angular momentum, addition of angular momentum, the Clebsch-Gordan coefficients, orbital angular momentum and parity.
		The spin angular momenta and the orbital angular momentum of the particles in the final state must add to give the angular momentum of the initial state.
		The possible values for the orbital angular momentum quantum number are l=1 and l=2.
	electron6.phys.utk.edu /phys594/archives/quantum/Angular/angular1.htm (653 words)

	The Russell Saunders Coupling Scheme
		Each orbital has a characteristic shape reflecting the motion of the electron in that particular orbital, this motion being characterised by an angular momentum that reflects the angular velocity of the electron moving in its orbital.
		This is found to give a good approximation for first row transition series where J coupling is ignored, however for elements with atomic number greater than thirty, spin-orbit coupling becomes more significant and the j-j coupling scheme is used.
		Coupling occurs between the resultant spin and orbital momenta of an electron which gives rise to J the total angular momentum quantum number.
	wwwchem.uwimona.edu.jm /courses/RScoupling.html (1201 words)

	[No title]
		As nonlinear optical processes of ever greater complexity become feasible and of interest, the construction of an efficient algorithm for determining these predictions is a useful goal, in view of the rapidly escalating difficulty of performing calculations when the number of vectors (polarisation or field) involved is greater than four.
		angular momentum coupling theory; the symmetries of the medium probably also require analysis of some subgroup of SO(3).
		Various algorithms for reducing angular momentum coupling trees have been developed, some with possible computer implementation in mind.
	cpc.cs.qub.ac.uk /summaries/ABRD_v1_0.html (334 words)

	Glossary
		Angular momentum A measure of the momentum associated with rotation around an axis; a vector, its direction determined by the axis.
		The law of conservation of momentum states that when two or more objects interact--a cannon fires a shell, a rocket shoots out a fast jet of hot gas, a bowling ball scatters a group of pins--the total vector sum of their momenta is unchanged.
		Spin of an electron, intrinsic angular momentum of an electron, affecting energy levels of atoms and such phenomena as the ordering of elements in the periodic table.
	www-spof.gsfc.nasa.gov /stargaze/Sgloss.htm (14613 words)

	Organic light-emitting diode - Wikipedia, the free encyclopedia
		The materials currently employed in the emissive layer are typically fluorophors, which can only emit light when a singlet exciton forms, which reduces the OLED's efficiency.
		Luckily, by incorporating transition metals into a small-molecule OLED, the triplet and singlet states can be mixed by spin-orbit coupling, which leads to emission from the triplet state.
		However, this emission is always redshifted, making blue light more difficult to achieve from a triplet excited state.
	en.wikipedia.org /wiki/OLED (1266 words)

	Angular Momentum (Site not responding. Last check: 2007-11-02)
		Overheads: Relation between the Coupled and the Uncoupled Representations
		Expansion of Coupled Wave Function in terms of the Uncoupled Representation & Clebsch-Gordon Coefficients
		The Quantum Mechanics of the Zeeman Effect on a Spin-Orbit Coupled Atom: Coupled and Uncoupled Representations
	www.chem.brown.edu /chem277/lect10.html (195 words)

	NIST: Methane Symmetry Operations - Irreducible Tensorial Sets
		The mathematical formalism developed for coupling and recoupling angular momenta in atoms [22, 29, 62] and in molecules [63] can be used advantageously when the molecular point group contains doubly and triply degenerate representations.
		One should thus resist the temptation to apply the formalism of vector coupling and recoupling developed for atoms to problems in methane without sufficient regard for the physical distinction between laboratory-fixed rotations and point-group rotations, or between the laboratory-fixed inversion operation and the molecule-fixed inversion operation.
		In the remainder of this section we shall discuss in general some of the ways in which irreducible tensor formalism can be applied to methane, without attempting to illustrate or to choose between the entire variety of notational and phase-factor conventions found in the group-theoretical literature and textbooks.
	physics.nist.gov /Pubs/Methane/chap16.html (468 words)

	Galaxy Collisions: 3. Transient Events I
		There is a great variety of disk waveforms, but the general structure of these waves depends more strongly on the angular momentum coupling than any other variable.
		However, there are a couple dozen collisional ring galaxies that have been studied in some detail, with many more candidates awaiting further study.
		Because of the limited resolution of the data, and the fact that dozens of foreground stars cover this galaxy, which lies near the galactic plane, this study was not definitive.
	www.public.iastate.edu /~curt/cg/section3.html (8045 words)

	Isomers.htm
		In contrast to shape isomers, which are due to a large change in deformation as seen in fission isomerism, spin and K isomers result from the angular momentum coupling of a few valence nucleons.
		Study of collective bands based on isomeric states is of considerable interest in order to understand the spin dependence of the goodness of the approximate symmetries leading to isomerism.
		of the angular momentum on the symmetry axis of a deformed nucleus appears to be approximately conserved as evidenced by the existence of
	www.pas.rochester.edu /~cline/Isomers.htm (575 words)

	[No title] (Site not responding. Last check: 2007-11-02)
		The topics selected for study in this 315-page research monograph are: - Connection between the angular momentum coupling (3-j) and recoupling (6-j and 9-j) coefficients and generalized hypergeometric functions of unit argument.
		- Polynomial (or non-trivial) zeros of angular momentum coefficients: - closed form, formal binomial expansions for the 3-j, 6-j and 9-j coefficients.
		The contents of this book supplement the results in L.C. Biedenharn and J.D. Louck, "Angular Momentum in Quantum Physics" and "Racah-Wigner Algebra in Quantum Physics", Encyclopaedia of Mathematics and its Applications, Vols.
	math.nist.gov /opsf/books/rao.html (334 words)

	The Softley Group - Research Interests
		A useful physical view is that the Rydberg electron takes a classical trajectory into the core region where it exchanges energy and angular momentum with the core, and emerges with different quantum numbers on an altered trajectory, while the core quantum numbers are also changed.
		The major advantage of MQDT is that it is able to treat the ionization continua and bound Rydberg states within a single formalism, while progress is also being made to include dissociation continua.
		Each Rydberg series and the associated ionization continuum forms a single "channel" which is labelled by the angular momentum quantum numbers of the Rydberg electron and the quantum numbers of the ion core.
	physchem.ox.ac.uk /~tps/research6.html (1757 words)

	OU Physics Virtual Tour - Classes (Site not responding. Last check: 2007-11-02)
		Topics in nonrelativistic quantum mechanics including the Heisenberg and Schroedinger pictures, Dirac formalism, angular momentum, bound states of spherically symmetric potentials, time independent perturbation theory; potential scattering.
		Time-dependent perturbation theory, electromagnetic interactions, spin and angular momentum coupling, symmetry and statistics, density matrix, multiparticle systems.
		Topics covered include special relativity; 3+1 and 4-dimensional Maxwell theory; charged particle and electromagnetic field Langrangians; conservation of energy, momentum and angular momentum; delta function sources and Green's function for Maxwell's theory.
	www.nhn.ou.edu /dept-tour/class.html (601 words)

	NIST: Atomic Spectros. - Atomic States, Shells, Configs
		The quantum number j represents the angular momentum obtained by coupling the orbital and spin angular momenta of an electron, i.e., j = l + s, so that j = l ±
		The central field approximation for a many-electron atom leads to wave functions expressed in terms of products of such one-electron states [2,3].
		In the central field approximation there exists no angular-momentum coupling between a closed subshell and an electron outside the subshell, since the net spin and orbital angular momenta of the subshell are both zero.
	physics.nist.gov /Pubs/AtSpec/node03.html (606 words)

	Marko Horbatsch (Site not responding. Last check: 2007-11-02)
		Class Test #3: Tuesday, December 3, in class; topics: angular momentum coupling, magnetic moments.
		Some formulae will be provided (e.g., the normalizing factors for the action of the raising/lowering angular momentum operators).
		Solved problems 14.2,14.4; do calculations of Clebsch-Gordan coefficients (e.g., j1=3/2 and j2=1/2 are coupling to total angular momentum J=1 with known z-projection M=0 [or M=1]) and verify with the worksheet Clebsch.mws.
	www.yorku.ca /marko/index4010.html (291 words)

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