TRANSFORMATION AMPLITUDES FOR VECTOR ADDITION OF ANGULAR MOMENTUM; (j3mm′|j3JM)

1952 ◽  
Vol 30 (3) ◽  
pp. 253-256 ◽  
Author(s):  
G. S. Colladay ◽  
R. E. Sells ◽  
D. L. Falkoff
Keyword(s):  
Angular Momentum ◽  
Quantum Mechanical ◽  
Angular Momenta ◽  
Vector Addition

The transformation amplitudes for the quantum-mechanical vector addition of angular momenta, [Formula: see text] are given.

Properties of spin and orbital angular momenta of light

2021 ◽  
Vol 36 (26) ◽  
Author(s):  
Arvind ◽  
S. Chaturvedi ◽  
N. Mukunda
Keyword(s):  
Angular Momentum ◽  
Physical Properties ◽  
Degree Of Freedom ◽  
Polarization Degree ◽  
Quantum Mechanical ◽  
Light Fields ◽  
Spin Part ◽  
Full Account ◽  
Angular Momenta ◽  
Definition Of

This paper analyses the algebraic and physical properties of the spin and orbital angular momenta of light in the quantum mechanical framework. The consequences of the fact that these are not angular momenta in the quantum mechanical sense are worked out in mathematical detail. It turns out that the spin part of the angular momentum has continuous eigenvalues. Particular attention is given to the paraxial limit, and to the definition of Laguerre–Gaussian modes for photons as well as classical light fields taking full account of the polarization degree of freedom.

scholarly journals Spin-decoupled metasurface for simultaneous detection of spin and orbital angular momenta via momentum transformation

2021 ◽  
Vol 10 (1) ◽  
Author(s):  
Yinghui Guo ◽  
Shicong Zhang ◽  
Mingbo Pu ◽  
Qiong He ◽  
Jinjin Jin ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Simultaneous Detection ◽  
Single Element ◽  
Single Shot ◽  
Single Spin ◽  
Dual Functional ◽  
Angular Momenta ◽  
Quadratic Phase ◽  
Mode Space ◽  
Optical Configuration

AbstractWith inherent orthogonality, both the spin angular momentum (SAM) and orbital angular momentum (OAM) of photons have been utilized to expand the dimensions of quantum information, optical communications, and information processing, wherein simultaneous detection of SAMs and OAMs with a single element and a single-shot measurement is highly anticipated. Here, a single azimuthal-quadratic phase metasurface-based photonic momentum transformation (PMT) is illustrated and utilized for vortex recognition. Since different vortices are converted into focusing patterns with distinct azimuthal coordinates on a transverse plane through PMT, OAMs within a large mode space can be determined through a single-shot measurement. Moreover, spin-controlled dual-functional PMTs are proposed for simultaneous SAM and OAM sorting, which is implemented by a single spin-decoupled metasurface that merges both the geometric phase and dynamic phase. Interestingly, our proposed method can detect vectorial vortices with both phase and polarization singularities, as well as superimposed vortices with a certain interval step. Experimental results obtained at several wavelengths in the visible band exhibit good agreement with the numerical modeling. With the merits of ultracompact device size, simple optical configuration, and prominent vortex recognition ability, our approach may underpin the development of integrated and high-dimensional optical and quantum systems.

scholarly journals The Angular Momentum of Brightest Cluster Galaxies

2012 ◽  
Vol 8 (S295) ◽  
pp. 229-229
Author(s):  
S. Brough ◽  
K.-V. Tran ◽  
A. von der Linden
Keyword(s):  
Angular Momentum ◽  
Cluster Galaxies ◽  
Angular Momenta ◽  
Brightest Cluster Galaxies

AbstractMassive Brightest Cluster Galaxies (BCGs) are observed to have a range of angular momenta, suggesting a variety of merging histories.

SYMMETRY DECOUPLING IN LINEAR ALGEBRAIC VARIATIONAL SCATTERING PROBLEMS

1995 ◽  
Vol 06 (01) ◽  
pp. 105-121
Author(s):  
MEISHAN ZHAO
Keyword(s):  
Angular Momentum ◽  
Variational Principle ◽  
Total Angular Momentum ◽  
Numerical Calculations ◽  
Quantum Mechanical ◽  
Matrix Elements ◽  
Scattering Problems ◽  
Identical Particles ◽  
Generalized Newton

This paper discusses the symmetry decoupling in quantum mechanical algebraic variational scattering calculations by the generalized Newton variational principle. Symmetry decoupling for collisions involving identical particles is briefly discussed. Detailed discussion is given to decoupling from evaluation of matrix elements with nonzero total angular momentum. Example numerical calculations are presented for BrH2 and DH2 systems to illustrate accuracy and efficiency.

scholarly journals Partial conservation law in a schematic single j shell model

2017 ◽  
Vol 26 (01n02) ◽  
pp. 1740021 ◽  
Author(s):  
Wesley Pereira ◽  
Ricardo Garcia ◽  
Larry Zamick ◽  
Alberto Escuderos ◽  
Kai Neergård
Keyword(s):  
Angular Momentum ◽  
Matrix Element ◽  
Shell Model ◽  
Linear Function ◽  
Conservation Law ◽  
Interaction Matrix ◽  
Stationary States ◽  
Interaction Matrix Element ◽  
Angular Momenta ◽  
Partial Conservation

We report the discovery of a partial conservation law obeyed by a schematic Hamiltonian of two protons and two neutrons in a [Formula: see text] shell. In our Hamiltonian, the interaction matrix element of two nucleons with combined angular momentum [Formula: see text] is linear in [Formula: see text] for even [Formula: see text] and constant for odd [Formula: see text]. It turns out that in some stationary states, the sum of the angular momenta [Formula: see text] and [Formula: see text] of the proton and neutron pairs is conserved. The energies of these states are given by a linear function of [Formula: see text]. The systematics of their occurrence is described and explained.

Notizen: Quantum Mechanical Calculation of Collision Integrals for HD

1971 ◽  
Vol 26 (11) ◽  
pp. 1926-1928 ◽  
Author(s):  
W. E. Köhler
Keyword(s):  
Scattering Amplitude ◽  
Quantum Mechanical ◽  
Collision Term ◽  
Tensor Polarization ◽  
Collision Integrals ◽  
First Order ◽  
Relaxation Coefficient ◽  
Angular Momenta ◽  
Experimental Values ◽  
Good Agreement

The magnetic Senftleben-Beenakker effect of the viscosity is mainly determined by two collision integrals of the linearized quantum mechanical Waldmann-Snider collision term, viz. by the relaxation coefficient of the tensor polarization of the molecular rotational angular momenta and by the coefficient which couples the friction pressure tensor and the tensor polarization. Starting from a simple nonspherical potential for HD, the scattering amplitude is evaluated analytically in first order distorted wave Born approximation and the two collision integrals are calculated for room temperature. A fairly good agreement with experimental values is found.

scholarly journals Calibration of the angular momenta of the minor planets in the solar system

2019 ◽  
Vol 630 ◽  
pp. A68 ◽  
Author(s):  
Jian Li ◽  
Zhihong Jeff Xia ◽  
Liyong Zhou
Keyword(s):  
Angular Momentum ◽  
Solar System ◽  
Total Angular Momentum ◽  
Physical Parameters ◽  
Minor Planets ◽  
The Sun ◽  
Relative Angle ◽  
Angular Momenta ◽  
Dwarf Planets ◽  
Invariable Plane

Aims. We aim to determine the relative angle between the total angular momentum of the minor planets and that of the Sun-planets system, and to improve the orientation of the invariable plane of the solar system. Methods. By utilizing physical parameters available in public domain archives, we assigned reasonable masses to 718 041 minor planets throughout the solar system, including near-Earth objects, main belt asteroids, Jupiter trojans, trans-Neptunian objects, scattered-disk objects, and centaurs. Then we combined the orbital data to calibrate the angular momenta of these small bodies, and evaluated the specific contribution of the massive dwarf planets. The effects of uncertainties on the mass determination and the observational incompleteness were also estimated. Results. We determine the total angular momentum of the known minor planets to be 1.7817 × 1046 g cm2 s−1. The relative angle α between this vector and the total angular momentum of the Sun-planets system is calculated to be about 14.74°. By excluding the dwarf planets Eris, Pluto, and Haumea, which have peculiar angular momentum directions, the angle α drops sharply to 1.76°; a similar result applies to each individual minor planet group (e.g., trans-Neptunian objects). This suggests that, without these three most massive bodies, the plane perpendicular to the total angular momentum of the minor planets would be close to the invariable plane of the solar system. On the other hand, the inclusion of Eris, Haumea, and Makemake can produce a difference of 1254 mas in the inclination of the invariable plane, which is much larger than the difference of 9 mas induced by Ceres, Vesta, and Pallas as found previously. By taking into account the angular momentum contributions from all minor planets, including the unseen ones, the orientation improvement of the invariable plane is larger than 1000 mas in inclination with a 1σ error of ∼50−140 mas.

Effects of the Method of Body Segment Parameter Estimation on Airborne Angular Momentum

1996 ◽  
Vol 12 (4) ◽  
pp. 413-430 ◽  
Author(s):  
Young-Hoo Kwon
Keyword(s):  
Parameter Estimation ◽  
Angular Momentum ◽  
Estimation Methods ◽  
Body Segment ◽  
Angular Momenta ◽  
Geometric Methods

Ten body segment parameter (BSP) estimation methods were selected to compute the BSPs of 3 collegiate male gymnasts: cadaver-based methods (Group C, 4 methods), mass scanning-based methods (Group M, 4 methods) and geometric methods (Group G, 2 methods). Angular momenta of nine double somersault with full twist H-bar dismounts performed by the 3 gymnasts were computed. Each trial was processed 10 times using 10 sets of BSPs obtained from the estimation methods. Intergroup and intermethod comparisons of the airborne angular momenta were made. It was concluded that the method of BSP estimation affected the magnitude of airborne angular momentum but did not affect the magnitude of angular momentum fluctuation during the airborne phase.

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