Dirac Equation for Electron Channeling

1987 ◽  
pp. 185-189
Author(s):  
H. Pilkuhn ◽  
A. H. Sørensen
Keyword(s):  
Dirac Equation ◽  
Electron Channeling

Electron Channeling Patterns

1977 ◽  
Vol 35 ◽  
pp. 12-13
Author(s):  
David C. Joy
Keyword(s):  
Electron Diffraction ◽  
Incidence Angle ◽  
Photographic Plate ◽  
Diffraction Effect ◽  
Angle Of Incidence ◽  
Bulk Single Crystal ◽  
Time Resolved ◽  
Electron Channeling ◽  
Spatially Resolved ◽  
Large Bulk

Electron channeling patterns (ECP) were first found by Coates (1967) while observing a large bulk, single crystal of silicon in a scanning electron microscope. The geometric pattern visible was shown to be produced as a result of the changes in the angle of incidence, between the beam and the specimen surface normal, which occur when the sample is examined at low magnification (Booker, Shaw, Whelan and Hirsch 1967).A conventional electron diffraction pattern consists of an angularly resolved intensity distribution in space which may be directly viewed on a fluorescent screen or recorded on a photographic plate. An ECP, on the other hand, is produced as the result of changes in the signal collected by a suitable electron detector as the incidence angle is varied. If an integrating detector is used, or if the beam traverses the surface at a fixed angle, then no channeling contrast will be observed. The ECP is thus a time resolved electron diffraction effect. It can therefore be related to spatially resolved diffraction phenomena by an application of the concepts of reciprocity (Cowley 1969).

Bosonic Symmetries, Solutions, and Conservation Laws for the Dirac Equation with Nonzero Mass

2013 ◽  
Vol 58 (6) ◽  
pp. 523-533 ◽  
Author(s):  
V.M. Simulik ◽  
◽  
I.Yu. Krivsky ◽  
I.L. Lamer ◽  
◽  
...  
Keyword(s):  
Dirac Equation ◽  
Conservation Laws

SPIN-SPIN INTERACTION IN ONE PARTICLE DIRAC EQUATION

1999 ◽  
Vol 4 (0) ◽  
pp. 66-68
Author(s):  
І. І. Гайсак ◽  
В. С. Морохович
Keyword(s):  
Dirac Equation ◽  
Spin Interaction

Introduction to Relativistic Quantum Chemistry

2007 ◽  
Author(s):  
Kenneth G. Dyall ◽  
Knut Faegri
Keyword(s):  
Dirac Equation ◽  
Quantum Chemistry ◽  
Relativistic Theory ◽  
Density Functional ◽  
Relativistic Quantum ◽  
Relativistic Effects ◽  
Basis Sets ◽  
Spin Orbit ◽  
Approximate Methods ◽  
Nonrelativistic Theory

This book provides an introduction to the essentials of relativistic effects in quantum chemistry, and a reference work that collects all the major developments in this field. It is designed for the graduate student and the computational chemist with a good background in nonrelativistic theory. In addition to explaining the necessary theory in detail, at a level that the non-expert and the student should readily be able to follow, the book discusses the implementation of the theory and practicalities of its use in calculations. After a brief introduction to classical relativity and electromagnetism, the Dirac equation is presented, and its symmetry, atomic solutions, and interpretation are explored. Four-component molecular methods are then developed: self-consistent field theory and the use of basis sets, double-group and time-reversal symmetry, correlation methods, molecular properties, and an overview of relativistic density functional theory. The emphases in this section are on the basics of relativistic theory and how relativistic theory differs from nonrelativistic theory. Approximate methods are treated next, starting with spin separation in the Dirac equation, and proceeding to the Foldy-Wouthuysen, Douglas-Kroll, and related transformations, Breit-Pauli and direct perturbation theory, regular approximations, matrix approximations, and pseudopotential and model potential methods. For each of these approximations, one-electron operators and many-electron methods are developed, spin-free and spin-orbit operators are presented, and the calculation of electric and magnetic properties is discussed. The treatment of spin-orbit effects with correlation rounds off the presentation of approximate methods. The book concludes with a discussion of the qualitative changes in the picture of structure and bonding that arise from the inclusion of relativity.

scholarly journals Virial identity and weak dispersion for the magnetic Dirac equation

2011 ◽  
Vol 95 (2) ◽  
pp. 137-150 ◽  
Author(s):  
Nabile Boussaid ◽  
Piero D'Ancona ◽  
Luca Fanelli
Keyword(s):  
Dirac Equation ◽  
Virial Identity

scholarly journals Photonic realization of the κ -deformed Dirac equation

2021 ◽  
Vol 104 (1) ◽  
Author(s):  
P. Majari ◽  
E. Sadurní ◽  
M. R. Setare ◽  
J. A. Franco-Villafañe ◽  
T. H. Seligman
Keyword(s):  
Dirac Equation

scholarly journals On the nonlinear Dirac equation on noncompact metric graphs

2021 ◽  
Vol 278 ◽  
pp. 326-357
Author(s):  
William Borrelli ◽  
Raffaele Carlone ◽  
Lorenzo Tentarelli
Keyword(s):  
Dirac Equation ◽  
Metric Graphs ◽  
Nonlinear Dirac Equation

scholarly journals The Dirac Electron Consistent with Proper Gravitational and Electromagnetic Field of the Kerr–Newman Solution

Galaxies ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 18
Author(s):  
Alexander Burinskii
Keyword(s):  
Electromagnetic Field ◽  
Quantum Theory ◽  
Gravitational Field ◽  
Dirac Equation ◽  
Higgs Field ◽  
Vacuum State ◽  
Relativistic String ◽  
Dirac Equations ◽  
Dirac Electron ◽  
Relativistic Scattering

The Dirac electron is considered as a particle-like solution consistent with its own Kerr–Newman (KN) gravitational field. In our previous works we considered the regularized by López KN solution as a bag-like soliton model formed from the Higgs field in a supersymmetric vacuum state. This bag takes the shape of a thin superconducting disk coupled with circular string placed along its perimeter. Using the unique features of the Kerr–Schild coordinate system, which linearizes Dirac equation in KN space, we obtain the solution of the Dirac equations consistent with the KN gravitational and electromagnetic field, and show that the corresponding solution takes the form of a massless relativistic string. Obvious parallelism with Heisenberg and Schrödinger pictures of quantum theory explains remarkable features of the electron in its interaction with gravity and in the relativistic scattering processes.

Sign in / Sign up

Export Citation Format

Share Document