scholarly journals Semiclassical Limit of the Dirac Equation and Spin Precession

2000 ◽  
Vol 282 (2) ◽  
pp. 420-431 ◽  
Author(s):  
Herbert Spohn
Keyword(s):  
Dirac Equation ◽  
Semiclassical Limit ◽  
Spin Precession

scholarly journals Dispersion Lemmas Revisited

VLSI Design ◽  
1999 ◽  
Vol 9 (4) ◽  
pp. 365-375
Author(s):  
I. Gasser ◽  
P. A. Markowich ◽  
B. Perthame
Keyword(s):  
Dirac Equation ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Semiclassical Limit ◽  
Kinetic Equations ◽  
Wigner Transform ◽  
Dirac Equations

We investigate regularizing dispersive effects for various classical equations, e.g., the Schrödinger and Dirac equations. After Wigner transform, these dispersive estimates are reduced to moment lemmas for kinetic equations. They yield new regularization results for the Schrödinger equation (valid up to the semiclassical limit) and the Dirac equation.

On semiclassical states of a nonlinear Dirac equation

2013 ◽  
Vol 143 (4) ◽  
pp. 765-790 ◽  
Author(s):  
Y. H. Ding ◽  
C. Lee ◽  
B. Ruf
Keyword(s):  
Dirac Equation ◽  
Semiclassical Limit ◽  
Limit Problem ◽  
Energy Solution ◽  
Nonlinear Dirac Equation ◽  
Least Energy Solution ◽  
Semiclassical States ◽  
Image Position ◽  
Least Energy Solutions ◽  
Least Energy

We study the semiclassical limit of the least energy solutions to the nonlinear Dirac equation for x ∈ ℝ3. We prove that the equation has least energy solutions for all ħ > 0 small, and, in addition, that the solutions converge in a certain sense to the least energy solution of the associated limit problem as ħ → 0.

The semiclassical limit of the intermediate scattering function

1996 ◽  
Vol 89 (4) ◽  
pp. 1203-1207
Author(s):  
S. BONELLA ◽  
G. CICCOTTI ◽  
D.F. COKER
Keyword(s):  
Semiclassical Limit ◽  
Scattering Function ◽  
Intermediate Scattering Function

SPIN PRECESSION AND PHASE DELAY TUNNELING TIMES

1988 ◽  
Vol 49 (C6) ◽  
pp. C6-17-C6-22 ◽  
Author(s):  
Z. HUANG ◽  
P. H. CUTLER ◽  
T. E. FEUCHTWANG ◽  
R. H. GOOD ◽  
Jr. ◽  
...  
Keyword(s):  
Phase Delay ◽  
Spin Precession ◽  
Tunneling Times

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
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