Theory of Quantum and Classical Connections In Modeling Atomic, Molecular And Electrodynamical Systems

1st Edition

Print ISBN: 9780124095021
eBook ISBN: 9780124104686
Imprint: Academic Press
Published Date: 4th October 2013
Page Count: 80
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Quantum and Classical Connections in Modeling Atomic, Molecular and Electrodynamic Systems is intended for scientists and graduate students interested in the foundations of quantum mechanics and applied scientists interested in accurate atomic and molecular models. This is a reference to those working in the new field of relativistic optics, in topics related to relativistic interactions between very intense laser beams and particles, and is based on 30 years of research. The novelty of this work consists of accurate connections between the properties of quantum equations and corresponding classical equations used to calculate the energetic values and the symmetry properties of atomic, molecular and electrodynamical systems, as well as offering applications using methods for calculating the symmetry properties and the energetic values of systems and the calculation of properties of high harmonics in interactions between very intense electromagnetic fields and electrons.

Key Features

  • Features detailed explanations of the theories of atomic and molecular systems, as well as wave properties of stationary atomic and molecular systems
  • Provides periodic solutions of classical equations, semi-classical methods, and theories of systems composed of very intense electromagnetic fields and particles
  • Offers models and methods based on 30 years of research


Physics researchers and scientists in molecular, atomic, optics, electromagnetics, and particle physics, and graduate students

Table of Contents

  • Introduction
  • Chapter 1. Connection Between Schrődinger and Hamilton–Jacobi Equations in the Case of Stationary Atomic and Molecular Systems
    • Abstract
    • 1.1 Initial Hypotheses
    • 1.2 Schödinger Equation, Wave Equation, and Characteristic Equation
    • 1.3 Equation of the Wave Surfaces
    • 1.4 Periodic Motion of the Wave Surfaces
    • 1.5 Generalized Bohr Quantization Relation for the C Curves
    • 1.6 The Stationarity Condition and the de Broglie Relations for Multidimensional Systems
    • 1.7 Properties of the Central Field Semiclassical Method
  • Chapter 2. Connection Between Klein–Gordon and Relativistic Hamilton–Jacobi Equations for Systems Composed of Electromagnetic Fields and Particles
    • Abstract
    • 2.1 Initial Hypotheses
    • 2.2 Connection Between the Klein–Gordon and Relativistic Hamilton–Jacobi Equations
    • 2.3 Demonstration of the Relation (2.9)
    • 2.4 Periodicity Property of the System Electron–Electromagnetic Field
    • 2.5 The Head-on Interaction Between Very Intense Elliptically Polarized Laser Beams and Relativistic Electron Beams, as a Source of Generation of Very Energetic Radiations
    • 2.6 Polarization Effects in the Interaction, at Arbitrary Angle, Between Very Intense Laser Beams and Relativistic Electron Beams
    • 2.7 Classical Approach of Interactions Between Very Intense Laser Beams and Atoms
    • 2.8 Common Properties of the Systems Analyzed in Chapters 1 and 2
  • Appendix A. Proof of Equation (1.37)
  • Appendix B. Relations for the Elliptic Motion. Equation of the Wave Surfaces for Hydrogenoid Systems
    • B.1 The First Domain, When r Increases from and
    • B.2 The Second Domain, When r Decreases from and
  • Bibliography


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