ON ANGULAR MOMENTUM

Schwinger, J

doi:10.2172/4389568

Title: ON ANGULAR MOMENTUM

Full Record
Other Related Research

Abstract

The commutation relations of an arbitrary angular momentum vector can be reduced to those of the harmonic oscillator. This provides a powerful method for constructing and developing the properties of angular momentum eigenvectors. In this paper many known theorems are derived in this way, and some new results obtained. Among the topics treated are the properties of the rotation matrices; the addition of two, three, and four angular momenta; and the theory of tensor operators.

Authors:: Schwinger, J

Publication Date:: 1952-01-26

Research Org.:: Harvard Univ., Cambridge, MA (United States); Nuclear Development Associates, Inc. (US)

Sponsoring Org.:: US Atomic Energy Commission (AEC) (US)

OSTI Identifier:: 4389568

Report Number(s):: NYO-3071
TRN: US200506%%295

DOE Contract Number:: AT(30-1)-862(b)

Resource Type:: Technical Report

Resource Relation:: Other Information: PBD: 26 Jan 1952

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; HARMONIC OSCILLATORS; ANGULAR MOMENTUM; COMMUTATION RELATIONS; EIGENVECTORS; OSCILLATIONS; ROTATION; TENSORS; MATHEMATICAL MODELS

Citation Formats


                    Schwinger, J. ON ANGULAR MOMENTUM.  United States: N. p., 1952. 
        Web.  doi:10.2172/4389568.

Copy to clipboard


                    Schwinger, J. ON ANGULAR MOMENTUM.  United States.  https://doi.org/10.2172/4389568

Copy to clipboard


                    Schwinger, J. 1952.  
        "ON ANGULAR MOMENTUM".  United States.  https://doi.org/10.2172/4389568.  https://www.osti.gov/servlets/purl/4389568.

Copy to clipboard


                    
@article{osti_4389568,

  title        = {ON ANGULAR MOMENTUM},

  author       = {Schwinger, J},

  abstractNote = {The commutation relations of an arbitrary angular momentum vector can be reduced to those of the harmonic oscillator. This provides a powerful method for constructing and developing the properties of angular momentum eigenvectors. In this paper many known theorems are derived in this way, and some new results obtained. Among the topics treated are the properties of the rotation matrices; the addition of two, three, and four angular momenta; and the theory of tensor operators.},

  doi          = {10.2172/4389568},

  url          = {https://www.osti.gov/biblio/4389568},
  journal      = {},
number       = ,

  volume       = ,

  place        = {United States},

  year         = {1952},

  month        = {1}

}

Copy to clipboard

Technical Report:

View Technical Report (5.47 MB)

https://doi.org/10.2172/4389568

Save / Share:

Export Metadata

Save to My Library

Similar records in OSTI.GOV collections:

THEORY OF ANGULAR MOMENTUM IN N-DIMENSIONAL SPACE

Technical Report Louck, J

The commutation relations for angular-momentum components in an N- dimensional Euclidean space are defined, and a set of independent mutually commuting angularmomertum operators is constructed. The simultaneous eigenvectors of these commuting operators are chosen as basic eigenvectors to obtain the matrix representations of the angular-momentum components. The eigenvalues of the commuting operators are found. The position of orbital angular momentum with respect to the general theory is illustrated. The eigenvalues of the N-dimensional isotropic harmonic oscillator Hamiltonian and the matrix representations of the coordinates and conjugate linear momenta of the oscillator are derived in the representation which diagonalizes the orbitalmore »« less
Theoretical studies in nuclear structure

Technical Report Marshalek, E

In this period, the work has centered on two topics. The first is the study of a novel type of collective rotation in which an atomic nucleus with an inversion-symmetric shape rotates uniformly about an axis that is not a principal axis of the quadrupole tensor of the density distribution. This mode is referred to as tilted rotation. By using the cranking model together with higher-order corrections, it was shown that tilted rotation is indeed possible, not only within a microscopic framework, but also within the framework of collective models such as the IBM. The maximum tilt angle of {pi}/4more »« less
https://doi.org/10.2172/6048868

Full Text Available
Theoretical studies in nuclear structure. Progress report, June 1, 1991--November 30, 1991

Technical Report Marshalek, E

In this period, the work has centered on two topics. The first is the study of a novel type of collective rotation in which an atomic nucleus with an inversion-symmetric shape rotates uniformly about an axis that is not a principal axis of the quadrupole tensor of the density distribution. This mode is referred to as tilted rotation. By using the cranking model together with higher-order corrections, it was shown that tilted rotation is indeed possible, not only within a microscopic framework, but also within the framework of collective models such as the IBM. The maximum tilt angle of {pi}/4more »« less
https://doi.org/10.2172/10107501

Full Text Available
REMARK ON THE EIGENVECTORS OF ANGULAR MOMENTUM OPERATORS

Journal Article Buchdahl, H - American Journal of Physics (U.S.)

Elementary treatrients of a single angular momentum having componerts J / sub k/ (k = 1, 2, 3) usually go as far as discussions of the spectra of these operators and the derivations of their standard, i.e., J/sup 2/, J/sub 3/- diagonal, representatives. On the other hand, the standard representatives of their eigenvectors are not usually obtained, leaving J/sub 3/ aside, for which the problem is trivial. ln fact, this part of the theory is most often dealt with only after a lengthy excursion into the theory of matrix representations. The representatives in question are obtained here by means ofmore »« less
https://doi.org/10.1119/1.1969135
Spin matrices for gravitons and the Humblet decomposition of the angular momentum of gravitational radiation in the linearized theory

Journal Article Crichton, J; Medina, T - General Relativity and Gravitation; (USA)

The authors develop spin matrices for a classical gravitational field in the linearized theory which satisfy angular-momentum commutation relations and are appropriate for a spin angular momentum of two. The same spin matrices come out of a decomposition of the angular momentum density of the linearized gravitational field into orbital and spin parts, similar to that carried out by Humblet for the electromagnetic field. To achieve this decomposition, they use the momentum density for the gravitational field obtained from the Landau-Lifshitz pseudo-tensor in the weak gravity limit. They not a formal connection between the spin angular momenta of gravitational andmore »« less

Similar Records