Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Adding angular momenta

Efstratios Manousakis

Published Nov 1, 2015• 1 citation
Publisher

Abstract

Abstract This chapter discusses addition of angular momentum. This implies that it discusses how to build eigenstates of the total angular momentum and its projection from eigenstates of the individual angular momenta and their projections. It discusses Clebsh–Gordan coefficients.
DOI
10.1093/acprof:oso/9780198749349.003.0024

Related papers

Addition of Angular Momenta

Масуд Чайчиан, Rolf Hagedorn

This chapter discusses the addition of angular momenta in the physicist’s way. From the considerations it follows that there are several ways to construct complete systems of commuting angular momentum observables. Belonging to two complete sets (two different ‘couplings’) of commuting angular momentum observables, there must exist a unitary transformation. For more than two angular momenta there will be more sets and more unitary transformations between the different couplings. The matrix elements of these transformations are called ‘recoupling coefficients’. They can be expressed by sums over products of Clebsch-Gordan coefficients (CGCs); this is to be expected from the fact that repeated coupling of two angular momenta generates any desired coupling scheme. It also is to be expected that the transformations between different coupling schemes become rapidly more complicated with growing numbers of subsystems. A powerful and elegant graphical representation for CGCs exists which can be used in the calculations of coupling of angular momenta.

CRC Press eBooks•Jul 14, 2023•0 citations

Addition of Angular Momenta

Walter Wilcox

Synopsis: General operator properties of angular momenta are recalled, and a physical motivation for adding them is given. The product and total angular momentum bases are defined. It is shown how to express one basis in terms of the other, and an explicit example of adding two spin 1/2 angular momenta is given. A further example consists of adding a general orbital angular momentum value to spin 1/2. These considerations are applied to perturbations in the hydrogen atom energy spectrum, where the correct choice for calculations is the total angular momentum basis.

CRC Press eBooks•Aug 23, 2019•1 citation

Addition of Angular Momenta

Walter Wilcox

Synopsis: General operator properties of angular momenta are recalled, and a physical motivation for adding them is given. ƒe product and total angular momentum bases are defined. It is shown how to express one basis in terms of the other, and an explicit example of adding two spin 1/2 angular momenta is given. A further example consists of adding a general orbital angular momentum value to spin 1/2. ƒese considerations are applied to perturbations in the hydrogen atom energy spectrum, where the correct choice for calculations is the total angular momentum basis.

CRC Press eBooks•Apr 19, 2016•0 citations

Angular Momentum

A. C. Sharma

This chapter covers various aspects of orbital, total, and spin angular momenta and the Clebsch-Gordon coefficients. An approach that is not found in many books, is used to derive eigenvalues of orbital angular momentum. The Pauli theory of spin half systems, addition of angular momenta, eigenfunctions of orbital angular momentum, computation of Clebsch-Gordon coefficients, solved examples, and unsolved exercises are included in the chapter. The basic purpose of the chapter has been to bring out the quantum mechanical importance of the theory of angular momenta with the use of essential mathematical derivations, which are self-consistent, and to adopt an elegant modern approach. Special mention on why orbital angular momentum cannot have non-integer values is made. The concept of spin angular momentum, which is purely a quantum mechanical quantity, is introduced in a simple and most convincing manner.

CRC Press eBooks•Jun 18, 2021•0 citations

Orbital angular momentum

Victor M. Galitski, Boris Mikhailovich Karnakov, Vladimir I Kogan +1 more

Abstract This chapter analyzes issues that deal with the general properties of angular momentum; angular momentum, l = 1; the addition of angular momenta; and tensor formalism in angular momentum theory.

•Feb 28, 2013•0 citations

Simple derivation of the vector addition coefficients

Ole Ulfbeck

Two simple operators are constructed in the product space of two angular momenta. Powers of the operators, when acting on selected product vectors, produce vectors with definite total angular momentum and thereby directly yield the vector addition coefficients in a symmetric form.

Journal of Mathematical Physics•Aug 1, 2007•2 citations
This chapter discusses the addition of angular momenta in the physicist’s way. From the considerations it follows that there are several ways to construct complete systems of commuting angular momentum observables. Belonging to two complete sets (two different ‘couplings’) of commuting angular momentum observables, there must exist a unitary transformation. For more than two angular momenta there will be more sets and more unitary transformations between the different couplings. The matrix elements of these transformations are called ‘recoupling coefficients’. They can be expressed by sums over products of Clebsch-Gordan coefficients (CGCs); this is to be expected from the fact that repeated coupling of two angular momenta generates any desired coupling scheme. It also is to be expected that the transformations between different coupling schemes become rapidly more complicated with growing numbers of subsystems. A powerful and elegant graphical representation for CGCs exists which can be used in the calculations of coupling of angular momenta.
Synopsis: General operator properties of angular momenta are recalled, and a physical motivation for adding them is given. The product and total angular momentum bases are defined. It is shown how to express one basis in terms of the other, and an explicit example of adding two spin 1/2 angular momenta is given. A further example consists of adding a general orbital angular momentum value to spin 1/2. These considerations are applied to perturbations in the hydrogen atom energy spectrum, where the correct choice for calculations is the total angular momentum basis.
Synopsis: General operator properties of angular momenta are recalled, and a physical motivation for adding them is given. ƒe product and total angular momentum bases are defined. It is shown how to express one basis in terms of the other, and an explicit example of adding two spin 1/2 angular momenta is given. A further example consists of adding a general orbital angular momentum value to spin 1/2. ƒese considerations are applied to perturbations in the hydrogen atom energy spectrum, where the correct choice for calculations is the total angular momentum basis.
This chapter covers various aspects of orbital, total, and spin angular momenta and the Clebsch-Gordon coefficients. An approach that is not found in many books, is used to derive eigenvalues of orbital angular momentum. The Pauli theory of spin half systems, addition of angular momenta, eigenfunctions of orbital angular momentum, computation of Clebsch-Gordon coefficients, solved examples, and unsolved exercises are included in the chapter. The basic purpose of the chapter has been to bring out the quantum mechanical importance of the theory of angular momenta with the use of essential mathematical derivations, which are self-consistent, and to adopt an elegant modern approach. Special mention on why orbital angular momentum cannot have non-integer values is made. The concept of spin angular momentum, which is purely a quantum mechanical quantity, is introduced in a simple and most convincing manner.