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

Semiclassical limit of the Dirac equation and spin precession

Herbert E. Spohn

Published Nov 16, 1999• 41 citations
OpenAlex

Abstract

Abstract. We study the Dirac equation with slowly varying external potentials. Using matrix-valued Wigner functions we prove that the electron follows with high precision the classical orbit and that the spin precesses The high precision experiments of the anomalous magnetic moment of the electron or the muon use in their interpretation the BMT equation for spin precession [1]. The derivation of Bargmann, Michel, and Telegdi [2] does not even mention quantum mechanics, however. Rather their arguments are

Related papers

Classical Motions of Spin-½ Particles

Kenneth Rafanelli, Ralph Schiller

From the WKB solutions to the squared Dirac equation we derive the classical trajectories and spin precessions originally postulated by Bargmann, Michel, and Telegdi for charged spin-\textonehalf{} particles. Identical equations of motion are obtained from the WKB solutions to the Dirac equation.

Physical Review•Jul 13, 1964•54 citations

Semiclassical Time Evolution and Trace Formula for Relativistic Spin-1/2 Particles

Jens Bolte, Stefan Keppeler

We investigate the Dirac equation in the semiclassical limit $\ensuremath{\Elzxh}\ensuremath{\rightarrow}0$. A semiclassical propagator and a trace formula are derived and are shown to be determined by the classical orbits of a relativistic point particle. In addition, two phase factors enter, one of which can be calculated from the Thomas precession of a classical spin transported along the particle orbits. For the second factor we provide an interpretation in terms of dynamical and geometric phases.

arXiv:quant-ph/9805041•Physical Review Letters•Sep 7, 1998•81 citations

Verification of the semiclassical method for an electron moving in a homogeneous magnetic field

Vladimir A Bordovitsyn, A. N. Myagkii

A procedure based on the semiclassical approximation for high energy levels is developed to yield solutions to the classical equation of charge motion and to the Bargmann-Michel-Telegdi spin equation. To this end, exact solutions to the Klein-Gordon and the Dirac-Pauli equations are used. The essence of the procedure under review is that the quantum state of a charged particle in a homogeneous magnetic field is represented as a superposition of states corresponding to the neighboring energy levels. As a consequence, the expectation values of the momentum and spin operators with respect to the resulting nonstationary wave function (packet) strictly obey the classical equations of charge motion and spin precession.

arXiv:math-ph/0103022•Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Sep 1, 2001•1 citation

Classical and quantum theories of spin

Fabián H. Gaioli, Edgardo T. Garcia Alvarez

A great effort has been devoted to formulate a classical relativistic theory of spin compatible with quantum relativistic wave equations. The main difficulty in order to connect classical and quantum theories rests in finding a parameter which plays the role of proper time at a purely quantum level. We present a partial review of several proposals of classical and quantum spin theories from the pioneer works of Thomas and Frenkel, revisited in the classical BMT work, to the semiclassical model of Barut and Zanghi [Phys. Rev. Lett. 52, 2009 (1984)]. We show that the last model can be obtained from a semiclassical limit of the Feynman proper time parametrization of the Dirac equation. At the quantum level we derive spin precession equations in the Heisenberg picture. Analogies and differences with respect to classical theories are discussed in detail. 1

•Jan 1, 1998•7 citations

On the relativistic concept of the Dirac's electron spin

Nizar Hamdan, A. Chamaa, José Luis López-Bonilla

Despite the success of the Dirac equation, the incorporation of the special theory of relativity into quantum mechanics predicts some paradoxes, like that the spin prediction from Dirac equation can be only identified with non- relativistic approximations (Pauli and Foldy-Wouthysen), as well as the spin predication is a relativistic quantum phenomena because the spin prediction is a necessary requirement of the relativistic quantum mechanics only. In this paper we show that the derivation of the spin and its magnetic moment can be done with a pure classical treatment. Since we start from the classical physical laws and the classical relativity principle to get the linear Schrödinger equation as a result the derivation of the spin and its magnetic moment can be done with a pure classical treatment. This approach result a Schrödinger equation, in which we show that the spin of the electron is a non relativistic quantum phenomenon too.

Latin American journal of physics education•Jan 1, 2008•1 citation

About spin precession in electromagnetic wave

Sergey L. Cherkas

It is shown that two ways of the description of the 1/2-spin precession in a circularly polarized electromagnetic wave: on the basis of the Bargmann-Michel-Telegdi equation and on the basis of the Dirac equation with Pauli term give the same result in the second order on the wave's field for arbitrary wave length.

arXiv:hep-ph/9903336•Mar 12, 1999•0 citations
Abstract. We study the Dirac equation with slowly varying external potentials. Using matrix-valued Wigner functions we prove that the electron follows with high precision the classical orbit and that the spin precesses The high precision experiments of the anomalous magnetic moment of the electron or the muon use in their interpretation the BMT equation for spin precession [1]. The derivation of Bargmann, Michel, and Telegdi [2] does not even mention quantum mechanics, however. Rather their arguments are
We investigate the Dirac equation in the semiclassical limit $\ensuremath{\Elzxh}\ensuremath{\rightarrow}0$. A semiclassical propagator and a trace formula are derived and are shown to be determined by the classical orbits of a relativistic point particle. In addition, two phase factors enter, one of which can be calculated from the Thomas precession of a classical spin transported along the particle orbits. For the second factor we provide an interpretation in terms of dynamical and geometric phases.
A procedure based on the semiclassical approximation for high energy levels is developed to yield solutions to the classical equation of charge motion and to the Bargmann-Michel-Telegdi spin equation. To this end, exact solutions to the Klein-Gordon and the Dirac-Pauli equations are used. The essence of the procedure under review is that the quantum state of a charged particle in a homogeneous magnetic field is represented as a superposition of states corresponding to the neighboring energy levels. As a consequence, the expectation values of the momentum and spin operators with respect to the resulting nonstationary wave function (packet) strictly obey the classical equations of charge motion and spin precession.
A great effort has been devoted to formulate a classical relativistic theory of spin compatible with quantum relativistic wave equations. The main difficulty in order to connect classical and quantum theories rests in finding a parameter which plays the role of proper time at a purely quantum level. We present a partial review of several proposals of classical and quantum spin theories from the pioneer works of Thomas and Frenkel, revisited in the classical BMT work, to the semiclassical model of Barut and Zanghi [Phys. Rev. Lett. 52, 2009 (1984)]. We show that the last model can be obtained from a semiclassical limit of the Feynman proper time parametrization of the Dirac equation. At the quantum level we derive spin precession equations in the Heisenberg picture. Analogies and differences with respect to classical theories are discussed in detail. 1
Despite the success of the Dirac equation, the incorporation of the special theory of relativity into quantum mechanics predicts some paradoxes, like that the spin prediction from Dirac equation can be only identified with non- relativistic approximations (Pauli and Foldy-Wouthysen), as well as the spin predication is a relativistic quantum phenomena because the spin prediction is a necessary requirement of the relativistic quantum mechanics only. In this paper we show that the derivation of the spin and its magnetic moment can be done with a pure classical treatment. Since we start from the classical physical laws and the classical relativity principle to get the linear Schrödinger equation as a result the derivation of the spin and its magnetic moment can be done with a pure classical treatment. This approach result a Schrödinger equation, in which we show that the spin of the electron is a non relativistic quantum phenomenon too.