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Training and Research

Matrix Method of Eigenvalue for the Addition of Angular Momenta

Shao Jian-jun

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

Matrix expression of quantum mechanics is discussed. Matrix method of eigenvalue for the addition of angular momenta is studied, and the most useful matrix eigenvalue method is discussed.

Related papers

Addition or arbitrary number of identical angular momenta

V V Mihailov

Under the vector addition of angular momenta, each equal to s, the resulting angular momentaj occur with some multiplicity. The general formula for these multiplicities is obtained by a simple algebraic method. In the case of s=1/2 the expression proves to be a well known one. Also given are some relations connected with the multiplicities.

Journal of Physics A Mathematical and General•Feb 1, 1977•29 citations

Adding angular momenta

Efstratios Manousakis

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.

•Nov 1, 2015•1 citation

Addition of arbitrary number of identical angular momenta

Mohammad A. Rashid

An alternate method is used to establish the analytic expression recently given and incompletely proved by Mikhailov (see ibid., vol.10, p.147 (1977)) for the multiplicity of occurrence of any angular momentum in the vector addition of n identical angular momenta.

Journal of Physics A Mathematical and General•Aug 1, 1977•9 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

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

Glover S. Colladay, R. E. Sells, David L. Falkoff

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

Canadian Journal of Physics•May 1, 1952•22 citations

Eigenvalues of J2

Kenneth R. Brownstein

Most derivations of the possible eigenvalues of J2 [i.e., h/2j (j + 1), j = 0, 1/2, 1, 3/2,...] rely upon the eigenvalues, h/m, of a component of J, say Jz. A derivation of the J2 eigenvalues is presented in which the concept of Jz eigenvalues does not appear. The derivation is based upon addition of angular momenta and the algebraic properties of the Pauli spin matrices.

American Journal of Physics•Sep 1, 1979•0 citations
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.