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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© 2014
Academic Press
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About the author

Alexandru Popa

Alexandru Popa received the Physicist Engineer degree from the Polytechnic University of Bucharest, Romania in 1966, the M. Sc degree from the University of California, Berkeley in 1972 and the Ph. D degree from the Polytechnic University of Bucharest, Romania in 1974. He is currently a Senior Researcher at the Laser Department, National Institute for Laser, Plasma and Radiation Physics, Institute of Atomic Physics, Bucharest.


"This third edition includes chapters by Martin Evans and Shinya Yamanaka, who were awarded the Nobel Prize in 2007 and 2012 respectively for their discoveries regarding embryonic stem cells. Writing for students and general readers, they and other scientists describe recent developments in both embryonic and adult stem cell research. They cover basic biology and mechanisms, tissue and organ development, methods, applications, and regulation and ethics.", February 2014