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 Mathematical Physics

Eigenvalues of S⋅Π for spins 1/2, 1, and 3/2

David Leo Weaver

Published Jan 1, 1978• 7 citations
Publisher

Abstract

The eigenvalues of the matrix operator S⋅Π for a constant magnetic field are derived in a parallel way for spins 1/2, 1, and 3/2 using only the algebra of the spin matrices and the commutation relations of the components of Π.
DOI
10.1063/1.523519

Related papers

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

Second Quantization Operators for Spin Operators

Takehiko Oguchi

Based on the commutation relations of spin operators, the second quantization operators derived by Holstein-Primakoff and Dyson and its Hermitean conjugate operators are obtained. The matrix representations for a scalar product of two spins by the Dyson's operators are not in agreement with the rigorous one except for the case of spin 1/2, although their eigenvalues are correct.

Journal of the Physical Society of Japan•Aug 15, 1992•0 citations

Spin Without Commutation Rules

Saul T. Epstein

The Pauli spin matrices are derived in a way which makes no appeal to the usual apparatus of abstract operators, commutation rules, etc.

American Journal of Physics•Sep 1, 1966•1 citation

An algebraic approach for a charged particle in a certain magnetic field

Mohammad Reza Setare, Ghafar Olfati

The properties of the charged particle in a certain varying magnetic field are outlined. A realization of the creation and annihilation operators for the wavefunctions is studied. It is shown that these operators satisfy the commutation relation of an SU(1,1) group. The closed analytical expressions for the matrix elements of different function ρ and ρ(d/dρ) are evaluated.

Physica Scripta•Jan 25, 2007•12 citations

A note on the eigenvalues of S.π for spin-1 in a constant magnetic field

J. Jayaraman, M Antonius, B de Oliveira

Exploiting the intimate connection of the problem of a charged spin-1 particle in a homogeneous magnetic field to that of a harmonic oscillator, it is demonstrated that the eigenvalues of the matrix operator S. pi for spin-1 and for a constant magnetic field are governed by a Hermitian matrix defined on the space of the particle number n and spin and are thus constrained to be real for any intensity of the external magnetic field H, thereby contradicting a recent affirmation of Weaver (1978) that for n=0, complex eigenvalues are present for sufficiently intense magnetic fields. The errors in Weaver's analysis which have led to complex eigenvalues as well as to an excessive number of eigenvalues compared with that demanded by the spin degrees of freedom are pointed out.

Journal of Physics A Mathematical and General•Oct 21, 1985•1 citation

A NOTE ON SOME PROPERTIES OF HAMILTONIANS INVOLVING SPIN MATRICES FOR HALF-INTEGRAL VALUES OF I

G. M. Volkoff

Canadian Journal of Physics•Aug 1, 1961•0 citations
Exploiting the intimate connection of the problem of a charged spin-1 particle in a homogeneous magnetic field to that of a harmonic oscillator, it is demonstrated that the eigenvalues of the matrix operator S. pi for spin-1 and for a constant magnetic field are governed by a Hermitian matrix defined on the space of the particle number n and spin and are thus constrained to be real for any intensity of the external magnetic field H, thereby contradicting a recent affirmation of Weaver (1978) that for n=0, complex eigenvalues are present for sufficiently intense magnetic fields. The errors in Weaver's analysis which have led to complex eigenvalues as well as to an excessive number of eigenvalues compared with that demanded by the spin degrees of freedom are pointed out.