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Topic: Orbital angular momentum vector

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  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).
The behavior of atoms and smaller particles is well described by the theory of quantum mechanics, in which each particle has an intrinsic angular momentum (or spin) and specific configurations of, e.g.
Angular momentum coupling is a category including some of the ways that subatomic particles can interact with each other.
en.wikipedia.org /wiki/Spin-orbit_coupling   (1244 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)

 angular_momentum_quantum_number   (Site not responding. Last check: 2007-10-14)
In atomic physics, an '''angular quantum momentum number''' is any of the quantum numbers that quantize an angular momentum.
In quantum mechanics, angular momenta of electrons (and also of other particles or systems of particles) are '''quantified vectors''', i.e., vectors whose allowed values are not constinuous but discrete, so their projections on an arbitrary axis differ in one unit of
The orbital angular momentum is parametrized by the azimuthal quantum number ''l'' and its ''z''-projection by the magnetic quantum number ''m
q-basic.xodox.de /angular_momentum_quantum_number   (417 words)

 Einstein-Cartan theory - Wikipedia, the free encyclopedia
Spin (intrinsic angular momentum) consists of dislocations in the fabric of spacetime.
It has long been known that the spin angular momentum tensor Spin(a,b,^k} is the "Noether current" of rotational symmetry of spacetime, and the momentum tensor P{a,k} is the Noether current of translational symmetry.
The momentum tensor P{a,^k} describe the flux of a-momentum through a flux box normal to the k-direction in spacetime, and the spin tensor Spin{a,b,^k} describes the flux of angular momentum in the a × b plane through a flux box normal to the k-direction in spacetime.
en.wikipedia.org /wiki/Einstein-Cartan_theory   (2408 words)

 Encyclopedia: S-orbital   (Site not responding. Last check: 2007-10-14)
The chemical properties of an atom are largely determined by the arrangement of the electrons in its outermost ("valence") shell (although other factors, such as atomic radius, atomic mass, and increased accessibility of additional electronic states also contribute to the chemistry of the elements as atomic size increases).
In hydrogen, that s orbital is in the lowest possible energy state of any atom, the first-shell orbital (and represented by hydrogen's position in the first period of the table).
The numbers are the shell number, n; the letters refer to the angular momentum state, as given above, and the superscripted numbers are the number of electrons in that state for the atom in question.
www.nationmaster.com /encyclopedia/S_orbital   (950 words)

 Azimuthal quantum number - Wikipedia, the free encyclopedia
The Azimuthal quantum number (or orbital angular momentum quantum number) l is a quantum number for an atomic orbital which determines its orbital angular momentum.
(which can be thought of [somewhat inaccurately] as the [quantised] projection of the angular momentum vector on the z-axis) runs from −l to l in integer units, and so there are 2l+1 possible states.
Orbitals with higher l than given in the table are perfectly permissible, but these values cover all atoms so far discovered.
en.wikipedia.org /wiki/azimuthal_quantum_number   (198 words)

 [No title]   (Site not responding. Last check: 2007-10-14)
Correspondingly, in the vicinity of C-points the orbital angular momentum arises and in the area of s-contours the spin angular momentum vanishes.
Momentum magnitude depends on the frequency of the vector rotation.
The magnitude of spin angular momentum, which is comparable with magnitude of one in the area of C-point may be obtained if the optical trap is formed by superposition of beams with different wave length.
www.photon04.org /Abstract/OPD15.3.5.doc   (298 words)

 Re: Quantisation of orbital angular momentum.   (Site not responding. Last check: 2007-10-14)
Standard textbook treatments of angular momentum show that for any vector operator J with commutation relations given by [J_1, J_2] = i hbar J_3 and its cyclic permutations J^2/hbar^2 is quantized in the form j(j + 1) and each component of J/hbar is quantized in corresponding half-integer units.
For orbital angular momentum L = r x p, we deduce the required commutation relations from [ r, p ] = i hbar, and then we note that invariance under 2 pi rotations implies that the quantization of L should be in integer units.
Under a shift of co-ordinates, the commutation relations [ r, p ] = i hbar and hence [L_1, L_2] = i hbar L_3 and its cyclic permutations are unchanged.
www.lns.cornell.edu /spr/2000-05/msg0024472.html   (309 words)

 Portrait - Angular Momentum
Innovative Angular Momentum Watches, With angular momentum, you have inertia, that with the angular velocity is continually active, relative to the rotational axis.
ANGULAR MOMENTUM is a concept taken from astrophysics that derives from the combination of a moment of inertia with an angular velocity.
ANGULAR MOMENTUM is a vector quantity, requiring the specification of both a magnitude and a direction for its complete description.
www.angularmomentum.com /e/portrait.e/portrait.e.html   (896 words)

 AIAS: Orbital Angular Momentum Of Light   (Site not responding. Last check: 2007-10-14)
Orbital and spin angular momentum of radiation and the photon in the context of O(3) electrodynamics are discussed extensively in The Enigmatic Photon series, see the indices to the volumes.
Angular momentum operators are also discussed extensively in the Enigmatic Photon series in the context of the Poincare group, and the Wigner little group of the Poincare group (throughout the five volumes).
In antisymmetrized general relativity the photon's orbital and spin angular momenta are described by the electric and magnetic components respectively of the Sachs electromagnetic field tensor, and this field tensor contains a longitudinal spin angular momentum proportional to B(3).
www.aias.us /pub/OAMLight/oamlight.html   (512 words)

 Orbital Angular Momentum   (Site not responding. Last check: 2007-10-14)
Angular momentum is actually a vector oriented perpendicular to the wire loop in the example we are discussing.
The direction of the vector is defined using a variation on the right-hand rule: Curl your fingers in the direction of motion of the bead around the loop (using your right hand!).
Figure 9.6 illustrates the angular momentum vector associated with a bead moving on a wire loop which is tilted from the horizontal.
www.physics.nmt.edu /~raymond/classes/ph13xbook/node103.html   (523 words)

 Quantized Angular Momentum
It is a characteristic of angular momenta in quantum mechanics that the magnitude of the angular momentum in terms of the orbital quantum number is of the form
The relationship between the magnitude of the angular momentum and its projection along any direction is space is often visualized in terms of a vector model.
When the orbital angular momentum and spin angular momentum are coupled, the total angular momentum is of the general form for quantized angular momentum
hyperphysics.phy-astr.gsu.edu /hbase/quantum/qangm.html   (343 words)

 Encyclopedia: Electron configuration
Electron atomic and molecular orbitals In atomic physics, an electron orbital (or simply orbital) is the description of the behavior of an electron in an atom or molecule according to quantum mechanics.
The actual magnetic dipole moment of an electron in an atomic orbital derives not only from the electron's angular momentum, but also from the electron spin, expressed in the spin quantum number.
In atomic physics, an electron subshell is a group of atomic orbitals with the same values of the principal quantum number n and the angular momentum quantum number l.
www.nationmaster.com /encyclopedia/Electron-configuration   (2227 words)

 Rigid Rotor
The central role of angular momentum in quantum mechanics is indicated by the fact that Planck's constant itself has units of angular momentum.
Angular momentum is a vector quantity that results from the cross-product of the position vector r from the center of rotation with the linear momentum vector p of the particles in motion.
These five d orbitals are normally degenerate but in the presence of a magnetic field they will separate into five different energies corresponding to the orientation of the angular momentum vector with the field.
cat.middlebury.edu /~chem/chemistry/class/physical/quantum/help/rigid_rotor/rigid_rotor.html   (1188 words)

 Total orbital angular momentum and total spin angular momentum (from spectroscopy) --  Encyclopædia Britannica   (Site not responding. Last check: 2007-10-14)
For atoms in the first three rows and those in the first two columns of the periodic table, the atom can be described in terms of quantum numbers giving the total orbital angular momentum and total spin angular momentum of a given state.
Angular momentum is a vector quantity, requiring the...
Momentum is equal to the product of the mass of an object multiplied by its velocity and is equivalent to the force required to bring the object to a stop in a unit...
www.britannica.com /eb/article?tocId=80612   (934 words)

 Intrinsic Wobble of Spinning Objects
In contrast, the wobble is just due to the free dynamics of the spinning Earth, due to the tilt between its angular momentum and it axis of symmetry.
Notice that the total angular velocity vector w makes an angle "b" with the z axis, and it also makes an angle a-b with the total H vector.
The axis of the latter is the H vector, and the axis of the former is the z axis.
www.mathpages.com /home/kmath116.htm   (390 words)

 Eccentricity vector - Encyclopedia.WorldSearch   (Site not responding. Last check: 2007-10-14)
In astrodynamics the eccentricity vector of a conic section orbit is the vector pointing towards the periapsis and with length equal to the orbit's scalar eccentricity.
is velocity vector of the orbital state vectors,
is position vector of the orbital state vectors,
encyclopedia.worldsearch.com /eccentricity_vector.htm   (95 words)

 Search Results for angular - Encyclopædia Britannica
In terms of classical physics, angular momentum is a property of a body that is in orbit or is...
The angular momentum of a particle of mass m moving with velocity v at the...
Let x denote the position vector of a point in space as measured relative to the origin of a Newtonian reference frame; x has the components (x1, x2, x3) relative to a Cartesian set of axes, which is...
www.britannica.com /search?query=angular&ct=&fuzzy=N   (500 words)

 Theory of Rotational Behavior of a Rocket Body   (Site not responding. Last check: 2007-10-14)
The spin-frequency and the angle between the axis of symmetry and the angular momentum are defined by the initial conditions, such as the force with which the rocket was disconnected from the payload.
In that case the angular momentum is perpendicular to the line of nodes of the satellite's orbit.
In this case the angular momentum vector is parallel to the Earth's rotation axis.
www.satobs.org /tumble/rottheory.html   (1460 words)

 MSc Physics of Advanced Semiconductor Materials - lecture 2
Angular momenta are vector quantities and it turns out that vector sums of the orbital and spin angular momenta are time independent since these vector sums represent the total angular momentum of the electron - and this is a 'constant of the motion'.
This is established by considering the sign of the wavefunction for the molecular orbital at a particular point and inverting through the centre of symmetry of the molecule until reaching the corresponding position on the other side.
Most electrons will be in the inner, most tightly bound, orbitals with their spins paired and contribute neither to the net orbital nor the net spin angular momentum of the molecule.
www.tlchm.bris.ac.uk /~paulmay/misc/msc/msc2.htm   (5937 words)

 [No title]   (Site not responding. Last check: 2007-10-14)
As in electromagnetic field theory, in an unpolarized sample the external components of angular momentum of the nuclei to be subjected to a kinemassic force field are originally randomly oriented such that the material exhibits no residual kinemassic field of its own.
The interaction of the spin nuclei angular momentum with inertial space causes the spin nuclei axes of the respective nuclei of the material being spun to tend to reorient parallel with the axis of the rotating member.
It is the average density of all the zones that determines the magnitude of the antiparallel field force vector in its opposition to the ambient gravitational field force vector.
www.fortunecity.com /greenfield/fatcat/53/wallace.html   (3794 words)

 [No title]   (Site not responding. Last check: 2007-10-14)
Classically and quantum mechanically, conservation of angular momentum is a consequence of the isotropy of space.
The angular momentum of a system which is not isolated may also be conserved in certain cases.
For example, the orbital angular momentum of a point particle moving in a central potential is conserved.
electron6.phys.utk.edu /qm1/modules/m11/angular.htm   (627 words)

 Spin Angular Momentum
The type of angular momentum discussed above is associated with the movement of particles in orbits.
e., the square of the spin angular momentum vector of a particle is
The spin angular momentum for an elementary particle is absolutely conserved, i.
physics.nmt.edu /~raymond/classes/ph13xbook/node104.html   (111 words)

 Answers 5
For a particle in the quantum state n,m of a square two-dimensional box of length L on each side, calculate the expectation value of the z-component of the angular momentum.
For a particle with angular momentum quantum number l=3, sketch the allowed orientations of the angular momentum vector, relative to the z-axis.
The angular momentum vector will be at an angle of 73.2 degrees relative to the z-axis.
classweb.gmu.edu /sdavis/chem332/Set5/answers5.htm   (542 words)

 [No title]
For hydrogenic atomic orbitals, ms, can only be ±1/2 E13.2(b): (a) A boundary surface for a hydrogenic orbital is drawn so as to contain most (say 90%) of the probability density if an electron in that orbital.
The energy of interaction is proportional to the scalar product of the two vectors representing the spin and orbital angular momenta and hence depends upon the orientation of the two vectors.
The total angular momentum of an electron in an atom is the vector sum of the orbital and spin angular momenta as illustrated in Fig.13.30 and expressed in eqn 13.46.
www.unlv.edu /faculty/nbala/problem_set13.doc   (784 words)

 Restless Mass
This is consistent with the previous result, i.e., the rest mass of two particles in equal and opposite motion about the center of the configuration is simply the sum of their (transverse) relativistic masses, i.e., the sum of their energies.
However, it does not follow that the components of its energy-momentum vector are all zero, because the Minkowskian norm is not positive-definite.
The Minkowski norms of each of these vectors individually are zero, but the sum of these two vectors is [2E, 0, 0, 0], which has a Minkowski norm of 2E.
www.mathpages.com /home/kmath232/kmath232.htm   (1479 words)

 Angular Momentum
To find the spin angular momentum, subdivide the object into small pieces of mass and find the angular momentum for each of the small pieces.
This radiation is produced at the expense of the rotational energy and the angular momentum is not strictly conserved---it slowly decreases.
The orbital angular momentum is conserved, so as the gas' distance from the compact companion DEcreases, its orbital speed must INcrease.
www.astronomynotes.com /angmom/s2.htm   (647 words)

 The Spin-Orbit Interaction in Sodium
The total angular momentum is conserved in all interaction and not necessairly L or S individually.
If the orbital angular momentum is not zero, then the orbital motion of the electron creates an internal magnetic field (Bint).
The 3p(1/2) state electrons on the other hand will be shifted to an energy level less than that of 3p since the angular momentum vectors more or less substract to give a smaller magnitude for the total angular momentum.
www.physics.sfsu.edu /~etapio/ph490/background.html   (766 words)

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