Variational Principles and Methods in Theoretical Physics and Chemistry

Variational Principles and Methods in Theoretical Physics and Chemistry
Author: Robert K. Nesbet
Publisher: Cambridge University Press
Total Pages: 245
Release: 2002-11-14
Genre: Science
ISBN: 1139435698

This book brings together the essential ideas and methods behind applications of variational theory in theoretical physics and chemistry. The emphasis is on understanding physical and computational applications of variational methodology rather than on rigorous mathematical formalism. The text begins with an historical survey of familiar variational principles in classical mechanics and optimization theory, then proceeds to develop the variational principles and formalism behind current computational methodology for bound and continuum quantum states of interacting electrons in atoms, molecules, and condensed matter. It covers multiple-scattering theory, including a detailed presentation of contemporary methodology for electron-impact rotational and vibrational excitation of molecules. The book ends with an introduction to the variational theory of relativistic fields. Ideal for graduate students and researchers in any field that uses variational methodology, this book is particularly suitable as a backup reference for lecture courses in mathematical methods in physics and theoretical chemistry.

Variational Principles in Classical Mechanics

Variational Principles in Classical Mechanics
Author: Douglas Cline
Publisher:
Total Pages:
Release: 2018-08
Genre:
ISBN: 9780998837277

Two dramatically different philosophical approaches to classical mechanics were proposed during the 17th - 18th centuries. Newton developed his vectorial formulation that uses time-dependent differential equations of motion to relate vector observables like force and rate of change of momentum. Euler, Lagrange, Hamilton, and Jacobi, developed powerful alternative variational formulations based on the assumption that nature follows the principle of least action. These variational formulations now play a pivotal role in science and engineering.This book introduces variational principles and their application to classical mechanics. The relative merits of the intuitive Newtonian vectorial formulation, and the more powerful variational formulations are compared. Applications to a wide variety of topics illustrate the intellectual beauty, remarkable power, and broad scope provided by use of variational principles in physics.The second edition adds discussion of the use of variational principles applied to the following topics:(1) Systems subject to initial boundary conditions(2) The hierarchy of related formulations based on action, Lagrangian, Hamiltonian, and equations of motion, to systems that involve symmetries.(3) Non-conservative systems.(4) Variable-mass systems.(5) The General Theory of Relativity.Douglas Cline is a Professor of Physics in the Department of Physics and Astronomy, University of Rochester, Rochester, New York.

Introduction To The Quantum World Of Atoms And Molecules

Introduction To The Quantum World Of Atoms And Molecules
Author: Jens Peder Dahl
Publisher: World Scientific Publishing Company
Total Pages: 476
Release: 2001-06-15
Genre: Science
ISBN: 9813102578

This invaluable book provides a balanced and integrated introduction to the quantum world of atoms and molecules. The underlying basis of quantum mechanics is carefully developed, with respect for the historical tradition and from a molecular angle. The fundamental concepts in the theory of atomic and molecular structure are thoroughly discussed, as are the central techniques needed in quantum-chemical applications. Special attention is paid to exposing and clarifying the common ground of Hartree-Fock theory and density-functional theory. Throughout the text, the discussion is pedagogically obliging and aims at simplicity and mathematical clarity, while avoiding the use of advanced mathematics. End-of-chapter problems supplement the main text.

Boundary and Eigenvalue Problems in Mathematical Physics

Boundary and Eigenvalue Problems in Mathematical Physics
Author: Hans Sagan
Publisher: Courier Corporation
Total Pages: 420
Release: 2012-04-26
Genre: Science
ISBN: 0486150925

Well-known text uses a few basic concepts to solve such problems as the vibrating string, vibrating membrane, and heat conduction. Problems and solutions. 31 illustrations.

Basic Physics Of Radiotracers

Basic Physics Of Radiotracers
Author: W. Earl Barnes
Publisher: CRC Press
Total Pages: 190
Release: 2017-09-29
Genre: Science
ISBN: 1351368990

The opportunity to present the physics of radioactive processes in some detail apart from topics such as instrumentation which conventionally compete with it for spacer is most welcome. The material is intended to give a fairly complete introduction to radiation physics to those who which to have more than a descriptive understanding of the subject. Although it is possible to work one’s way through much of the subject matter without having any previous physics background, some prior acquaintance with modern physics is desirable. A familiarity with calculus and differential equations is also assumed. Volume I begins with a brief description of classical physics, it’s extension to special relativity and quantum mechanics, and an introduction to basic atomic and nuclear concepts. A thorough discussion of atomic structure follows with emphasis on the theory of the multielectron atom, characteristic X-rays, and the Auger effect. Volume II treats the subjects of nuclear structure, nuclear decay processes, the interaction of radiation with matter, and the mathematics of radioactive decay.

An Introduction to Quantum Theory

An Introduction to Quantum Theory
Author: Frank S. Levin
Publisher: Cambridge University Press
Total Pages: 812
Release: 2002
Genre: Science
ISBN: 9780521598415

An undergraduate introductory quantum mechanics textbook with a large number of figures and exercises.

Variational Methods with Applications in Science and Engineering

Variational Methods with Applications in Science and Engineering
Author: Kevin W. Cassel
Publisher: Cambridge University Press
Total Pages: 433
Release: 2013-07-22
Genre: Mathematics
ISBN: 1107022584

This book reflects the strong connection between calculus of variations and the applications for which variational methods form the foundation.