aqora

Companion to Angular momentum

Valeria D. Kleiman

Angular Momentum Operators and Wave Functions. Coupling of Two Angular Momentum Vectors. Transformation Under Rotation. Coupling of More Than Two Angular Momentum Vectors. Spherical Tensor Operators. Energy-Level Structure and Wave Functions of a Rigid Rotor. Errata to 2nd Printing of Angular Momentum.

Wiley eBooksJan 1, 19989 citations

Angular-Momentum and Spherical Tensor Operators

Ingvar Lindgren, John Morrison

Springer eBooksJan 1, 19860 citations

Angular Momentum Operators and Their Matrix Elements

Springer eBooksJan 1, 20020 citations

Matrix Elements of Tensor Operators

D.M. Brink, G.R. Satchler

Abstract WE are now in a position to calculate those parts of any physical problem which are concerned with angular integrations, the coupling of angular momentum vectors, or our choice of coordinate system-in fact general rotational symmetries-which we might call the ‘geometrical’ parts. The basic technique is to exploit the simplest matrix reduction which we have, already met in Chapter IV, namely the WignerEckart theorem for the matrix elements of spherical tensors.

Feb 10, 19940 citations

Alternative Formulations for Angular Momentum Operators, Cartesian and Spherical Polar Forms

Carl W David

The conversion between representations of angular momentum in spherical polar and cartesian form is discussed.

Jan 1, 20060 citations

A new boson realization for the isotropic three-dimensional oscillator

Eugene R. Marshalek

Two new closely related boson realizations of the Heisenberg–Weyl algebra are derived that are directly equivalent to the introduction of spherical coordinates for the isotropic three-dimensional harmonic oscillator. This provides another way to obtain matrix elements of all physical operators connecting angular-momentum eigenstates, which are represented here by simple products of boson operators acting on the vacuum. Two of these bosons carry the angular-momentum quantum numbers while the third is a novel ‘‘radial boson.’’ In this approach, one begins by finding the nonunitary Dyson and then the unitarized Holstein–Primakoff realizations for the spectrum-generating SU(1,1)×SO(3) algebra of the oscillator. The corresponding mappings of the Heisenberg–Weyl generators are then obtained from their tensor properties under SU(1,1)×SO(3). The Dyson map of the Heisenberg–Weyl generators is not uniquely determined in this way, but the Holstein–Primakoff map is nevertheless unique. The possibility exists for generalization to isotropic oscillators of higher dimension, which are of interest in connection with nuclear collective motion.Two new closely related boson realizations of the Heisenberg–Weyl algebra are derived that are directly equivalent to the introduction of spherical coordinates for the isotropic three-dimensional harmonic oscillator. This provides another way to obtain matrix elements of all physical operators connecting angular-momentum eigenstates, which are represented here by simple products of boson operators acting on the vacuum. Two of these bosons carry the angular-momentum quantum numbers while the third is a novel ‘‘radial boson.’’ In this approach, one begins by finding the nonunitary Dyson and then the unitarized Holstein–Primakoff realizations for the spectrum-generating SU(1,1)×SO(3) algebra of the oscillator. The corresponding mappings of the Heisenberg–Weyl generators are then obtained from their tensor properties under SU(1,1)×SO(3). The Dyson map of the Heisenberg–Weyl generators is not uniquely determined in this way, but the Holstein–Primakoff map is nevertheless unique. The possibility exists for generalization to isotropic oscillators of higher dimension, which are of interest in connection with nuclear collective motion.

Journal of Mathematical PhysicsSep 1, 19926 citations

The use of `operator equivalents'

Abstract

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The use of `operator equivalents'

Abstract

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