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

Physics Letters A

Quantum theory of magnetic electron lenses based on the Dirac equation

R. Jagannathan, R. Simon, E. C. G. Sudarshan, Narasimhaiengar Mukunda

Published Jan 1, 1989• 66 citations
Publisher
DOI
10.1016/0375-9601(89)90685-3

Related papers

Quaternionic Electron Theory: Dirac's Equation

Stefano De Leo, Waldyr A. Rodrigues

International Journal of Theoretical Physics•May 1, 1998•37 citations

Quantum theory of electron lenses based on the Dirac equation

R. Jagannathan

The quantum theory of a magnetic electron lens with rotational symmetry about its straight optic axis has recently been studied entirely on the basis of the Dirac equation [R. Jagannathan, R. Simon, E. C. G. Sudarshan, and N. Mukunda, Phys. Lett. A 134, 457 (1989)]. Following the same type of algebraic approach, the present paper elaborates on the quantum mechanics of beam transport through a general electron-lens system with a straight axis. The basic theory is developed in a general framework, and examples of applications are treated under the paraxial approximation and thin-lens assumption. Extension of the theory to systems with curved optic axes is dealt with very briefly. The present formalism based on a ``beam-optical'' representation of the Dirac equation goes over directly to the Hamiltonian formalism of geometrical electron optics upon classicalization.

Physical Review A•Dec 1, 1990•62 citations

Electron Matter Optics and the Quantum Electron Stern-Gerlach Magnet

Scot McGregor, Roger Bach, Xiaolu Yin +3 more

Bulletin of the American Physical Society•Jun 16, 2011•0 citations

Field-theoretical methods in quantum magnetism

D. C. Cabra, Pierre Pujol

Lecture notes in physics•Jan 1, 2004•22 citations

Quantum theory of magnetic quadrupole lenses for spin-1/2 particles

Sameen Ahmed Khan

General guidelines for constructing a quantum theory of charged-particle beam optics starting ab initio from the basic equations of quantum mechanics, appropriate to the situation under study. In the context of spin-1/2 particles, these guidelines are used starting with the Dirac equation. The spinor theory just constructed is used to obtain the transfer maps for normal and skew magnetic quadrupoles respectively. As expected the traditional transfer maps get modified by the quantum contributions. The classical limit of the quantum formalism presented, reproduces the well-known Lie algebraic formalism of charged-particle beam optics.

arXiv:physics/9809032•Sep 21, 1998•10 citations

Local observables in the Dirac theory

David Hestenes

By a new method, the Dirac electron theory is completely reexpressed as a set of conservation laws and constitutive relations for local observables, describing the local distribution and flow of mechanical quantities. The coupling of the electromagnetic field to the electron is shown to be determined by the definitions of the observables rather than by the Dirac equation. Planck's constant appears in the equations only in connection with the electron spin. The equations are most readily interpreted by assuming that the electron is a structureless point charge, the spin and magnetic moment arising from the dynamics of electron motion.

Journal of Mathematical Physics•Jul 1, 1973•108 citations
The quantum theory of a magnetic electron lens with rotational symmetry about its straight optic axis has recently been studied entirely on the basis of the Dirac equation [R. Jagannathan, R. Simon, E. C. G. Sudarshan, and N. Mukunda, Phys. Lett. A 134, 457 (1989)]. Following the same type of algebraic approach, the present paper elaborates on the quantum mechanics of beam transport through a general electron-lens system with a straight axis. The basic theory is developed in a general framework, and examples of applications are treated under the paraxial approximation and thin-lens assumption. Extension of the theory to systems with curved optic axes is dealt with very briefly. The present formalism based on a ``beam-optical'' representation of the Dirac equation goes over directly to the Hamiltonian formalism of geometrical electron optics upon classicalization.
General guidelines for constructing a quantum theory of charged-particle beam optics starting ab initio from the basic equations of quantum mechanics, appropriate to the situation under study. In the context of spin-1/2 particles, these guidelines are used starting with the Dirac equation. The spinor theory just constructed is used to obtain the transfer maps for normal and skew magnetic quadrupoles respectively. As expected the traditional transfer maps get modified by the quantum contributions. The classical limit of the quantum formalism presented, reproduces the well-known Lie algebraic formalism of charged-particle beam optics.
By a new method, the Dirac electron theory is completely reexpressed as a set of conservation laws and constitutive relations for local observables, describing the local distribution and flow of mechanical quantities. The coupling of the electromagnetic field to the electron is shown to be determined by the definitions of the observables rather than by the Dirac equation. Planck's constant appears in the equations only in connection with the electron spin. The equations are most readily interpreted by assuming that the electron is a structureless point charge, the spin and magnetic moment arising from the dynamics of electron motion.