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

Journal of Kashgar Teachers College

Matrix Representation about Spin Angular Momentum Operator and Eigenvector on System of Double Electrons

Jianwei Wang

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

Express in self representation about spin angular momentum Operator,eigenvector on system of double electrons and transformation each other about ^S_z,^S_x,^S_y representation have been discussed with the theory of representation.We have got succinct practical express form.

Related papers

Matrix Representation about Orbit Angular Momentum Operator and Eigenvector of p Electron

Jianwei Wang

Express in self representation about the orbit angular momentum Operator,eigenvector of p electron in hydrogen atom and transformation each other about mechanics quantity representation have been discussed with the theory of representation.We have got succinct practical express form.

Journal of Kashgar Teachers College•Jan 1, 2005•0 citations

Matrix Representation about Orbit Angular Momentum Operator and Eigenvector of Delectron in Hydrogen Atom

Liu Na

We have got the Matrix representation of delectron in hydrogen atom about orbit angular momentum operator and eigenvector in Lz representation,resolved the problem of eigenvector about the operators of Lx and Ly.

Journal of Kashgar Teachers College•Jan 1, 2008•0 citations

Remark on the Eigenvectors of Angular Momentum Operators

H. A. Buchdahl

Elementary treatments of a single angular momentum having components Jk (k =1, 2, 3) usually go as far as discussions of the spectra of these operators and the derivations of their standard, i.e., J2, J3-diagonal, representatives. On the other hand, the standard representatives of their eigenvectors are not usually obtained, leaving J3 aside, for which the problem is trivial. In 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, in the first part of this paper, by means of essentially elementary arguments. Once these representatives are known, the standard representative of the unitary operator U which generates the state vector of a system after it has undergone a rotation R from the state vector prior to the rotation are deduced; this representative comprises just the familiar matrix representations of the rotation group. Finally, the relevance of harmonic oscillator theory to the present problem is briefly considered.

American Journal of Physics•Nov 1, 1963•3 citations

The Determination of Eigenvalues and Eigenvectors of the Orbital Angular Momentum

Kishwar Mohammed WASMAN, Saman MAWLUD

The theory of angular momentum performance a significant position in the classical and quantum mechanical study of physical properties, such as studies into nuclear, atomic, and molecular processes, as well as other quantum problems, including spherical symmetry. In this analysis, angular momentum operators are described in multiple ways, based on the angular momentum operator's commutator, matrix, and geometric representation, The eigenvalue and eigenvector were also known for operatorsJ ̂_±,J ⃑ ̂^2, J ̂_x,J ̂_y and J ̂_zwithin the |j,┤ ├ m⟩ basis. Furthermore, in quantum mechanics, angular momentum is called quantized variable, meaning that it comes in discrete quantities. In contrast to the macroscopic system case where a continuous variable is angular momentum.

Journal of Physical Chemistry and Functional Materials•Jun 28, 2022•0 citations

Angular Momentum Operators in Orthogonal Curvilinear Coordinate Systems

Sun Shu-sheng

Using the transformation matrix between the unit basis vectors in deferent orthogonal curvilinear coordinate systems,we deduce the general form of the transformation between the angular momentum operators in these coordinate systems.We give the representations of Hamilton operator  and angular momentum operators in the orthogonal curvilinear coordinate system.We discuss the transformation matrix of unit basis vectors among the spherical coordinate system,cylindrical coordinates system and rectangular coordinates system,and the transformation between the angular momentum operators.Furthermore,we discuss the treatment of 2operator in different coordinate systems.

Journal of Shenyang University of Chemical Technology•Jan 1, 2010•0 citations

The exact meaning of the angular-momentum and spin operators in quantum mechanics

G. Coddens

The theory of angular momentum and spin in quantum mechanics seems to defy common-sense intuition.We render the theory intelligible again by pointing out that this apparent impenetrability merely stems from an {\em undue} parallel interpretation of the algebraic expressions for the angular-momentum and spin operators in the group representation theory of SO(3) and SU(2). E.g. the correct meaning of the quantumoperator ${\hat{L}}_{z} = {\hbar\over{\imath}}\,(x{\partial\over{\partial y}} - y{\partial\over{\partial x}} )$ is not that it is the operatorfor the $z$-component $L_{z}$ of the angular momentum ${\mathbf{L}}$, but rather the expression of the operator for the angular momentum ${\mathbf{L}}$ when it is aligned with the $z$-axis. Hence what we are used to note (erroneously) as ${\hat{L}}_{z}$ is not a scalar but a vector operator.The same applies{\em mutatis mutandis} for the spin operators. In the correct interpretation, the wholealgebraic formalism is just the group representation theory for the rotationsof three-dimensional Euclidean geometry. It is thus mere,elementary high-school mathematics (in a less usual, more technical guise) and as such totally exempt of any physics, let alone quantum mysteries.The change of interpretation has no impact on the algebraic results, such that they remain in agreement with experimental data and the algebra quantum mechanics remains correct. It is all only a matter of the correct geometrical meaning of the algebra.All these statements are proved within the framework of the group representation theory for SO(3) and SU(2) which is the basic tool used to describe rotational motion in quantum mechanics.

•Sep 11, 2021•0 citations
Elementary treatments of a single angular momentum having components Jk (k =1, 2, 3) usually go as far as discussions of the spectra of these operators and the derivations of their standard, i.e., J2, J3-diagonal, representatives. On the other hand, the standard representatives of their eigenvectors are not usually obtained, leaving J3 aside, for which the problem is trivial. In 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, in the first part of this paper, by means of essentially elementary arguments. Once these representatives are known, the standard representative of the unitary operator U which generates the state vector of a system after it has undergone a rotation R from the state vector prior to the rotation are deduced; this representative comprises just the familiar matrix representations of the rotation group. Finally, the relevance of harmonic oscillator theory to the present problem is briefly considered.
The theory of angular momentum performance a significant position in the classical and quantum mechanical study of physical properties, such as studies into nuclear, atomic, and molecular processes, as well as other quantum problems, including spherical symmetry. In this analysis, angular momentum operators are described in multiple ways, based on the angular momentum operator's commutator, matrix, and geometric representation, The eigenvalue and eigenvector were also known for operatorsJ ̂_±,J ⃑ ̂^2, J ̂_x,J ̂_y and J ̂_zwithin the |j,┤ ├ m⟩ basis. Furthermore, in quantum mechanics, angular momentum is called quantized variable, meaning that it comes in discrete quantities. In contrast to the macroscopic system case where a continuous variable is angular momentum.
Using the transformation matrix between the unit basis vectors in deferent orthogonal curvilinear coordinate systems,we deduce the general form of the transformation between the angular momentum operators in these coordinate systems.We give the representations of Hamilton operator  and angular momentum operators in the orthogonal curvilinear coordinate system.We discuss the transformation matrix of unit basis vectors among the spherical coordinate system,cylindrical coordinates system and rectangular coordinates system,and the transformation between the angular momentum operators.Furthermore,we discuss the treatment of 2operator in different coordinate systems.
The theory of angular momentum and spin in quantum mechanics seems to defy common-sense intuition.We render the theory intelligible again by pointing out that this apparent impenetrability merely stems from an {\em undue} parallel interpretation of the algebraic expressions for the angular-momentum and spin operators in the group representation theory of SO(3) and SU(2). E.g. the correct meaning of the quantumoperator L^z=ℏı (x∂∂y−y∂∂x){\hat{L}}_{z} = {\hbar\over{\imath}}\,(x{\partial\over{\partial y}} - y{\partial\over{\partial x}} )L^z​=ℏ​(x∂y∂​−y∂x∂​) is not that it is the operatorfor the zzz-component LzL_{z}Lz​ of the angular momentum L{\mathbf{L}}L, but rather the expression of the operator for the angular momentum L{\mathbf{L}}L when it is aligned with the zzz-axis. Hence what we are used to note (erroneously) as L^z{\hat{L}}_{z}L^z​ is not a scalar but a vector operator.The same applies{\em mutatis mutandis} for the spin operators. In the correct interpretation, the wholealgebraic formalism is just the group representation theory for the rotationsof three-dimensional Euclidean geometry. It is thus mere,elementary high-school mathematics (in a less usual, more technical guise) and as such totally exempt of any physics, let alone quantum mysteries.The change of interpretation has no impact on the algebraic results, such that they remain in agreement with experimental data and the algebra quantum mechanics remains correct. It is all only a matter of the correct geometrical meaning of the algebra.All these statements are proved within the framework of the group representation theory for SO(3) and SU(2) which is the basic tool used to describe rotational motion in quantum mechanics.