Theoretical and Quantum Mechanics: Fundamentals for Chemists

ISBN-13: 9781402033650 / Angielski / Twarda / 2005 / 513 str.

Stefan Ivanov

Opis

This book has emerged from an undergraduate course as well as a graduate one, which I have taught for a number of years. Recently, many universities have experimented by bringing quantum theory forward in the curriculum and we follow their example. This book is intended to serve as an introduction to theoretical mechanics and quantum mechanics for chemists. I have included those parts of quantum mechanics which are of greatest fundamental interest and utility, and have developed those parts of classical mechanics which relate to and illuminate them. I try to give a comprehensive treatment wherever possible. The book would acquaint chemists with the quantum structure of the basic object of chemistry, the atom. My intention is to bridge the gap between classical physics, general and inorganic chemistry, and quantum mechanics. For these reasons: 1. I present in one course the basics of theoretical mechanics and quantum mechanics, to emphasise the continuity between them; 2. I have chosen the topics of theoretical mechanics based upon two criteria: a) usefulness for chemical problems: two-body problem; rotational motion of a charged particles (free and in an atom); interaction of a magnetic field with a magnetic dipole; details of small oscillations and oscillations of molecules; b) the need for transition from classical to quantum mechanics: basics of Lagrangian mechanics; basics of Hamiltonian mechanics; 3. I give detailed explanation of an application of the quantum method to simple systems: one-dimensional potential, harmonic oscillator, hydrogen atom, and hydrog- like atoms.

Recenzje

"I like the approach followed very much. [...] He shows clearly that these more advanced and powerful methods can be straightforwardly applied to these problems. His transparant and elegant way of presentation will bring a deeper and more bountiful insight to the student in classical and quantum mechanics[...]"
(Steven Stolte, Department of Chemistry, Vrije Universiteit, The Netherlands)
"[...]I think it is a very useful book to have on my bookshelves, especially since it makes a clear connection between classical and quantum mechanics. [...]it is very useful for me and theoretically oriented chemists [...]I found the book very useful in preparing my lectures for my first-year quantum chemistry course as it gave me more insight into the connection between quantum and classical mechanics."
(Joop van Lenthe, Theoretical Chemistry Group, Utrecht University, The Netherlands)

Spis treści

PART ONE: SELECTED TOPICS OF THEORETICAL MECHANICS 1. LAGRANGIAN FUNCTION AND LAGRANGE’S EQUATIONS 2. CONSERVATION LAWS 3. CENTRAL CONSERVATIVE FORCES 4. ROTATING MOTION OF A CHARGED PARTICLE 5. SMALL HARMONIC OSCILLATIONS 6. HAMILTONIAN MECHANICS PART TWO: BASICS OF QUANTUM MECHANICS 7. THE SOURCES OF THE QUANTUM MECHANICS 8. OLD QUANTUM MECHANICS 9. THE WAVE FUNCTION 10. OPERATORS 11. THE SCHROEDINGER EQUATION AND TIME DEPENDENCE OF THE OBTHERVABLES 12. MOTION IN ONE-DIMENTIONAL POTENTIAL 13. THE HARMONIC QUANTUM OSCILLATOR 14. THE TWO-BODY PROBLEM – THE HYDROGEN ATOM AND A DIATOMIC MOLECULE 15. PERTURBATION THEORY AND STARK EFFECT 16. SPIN 17. INTERACTION OF ELECTRONS WITH MAGNETIC FIELD 18. THE HELIUM ATOM 19. PERIODIC TABLE

Blurb

Theoretical and Quantum Mechanics: Fundamentals provides an introduction to theoretical and quantum mechanics for chemists. The book includes carefully selected quantum mechanics topics of the most fundamental interest and use for chemists and classical mechanics topics that relate and illuminate these. A comprehensive treatment is given wherever possible. The book acquaints the chemists with the quantum structure of the basic object of chemistry – the atom – and the author bridges the gap between classical physics, general and inorganic chemistry, and quantum mechanics.

The book provides the basics of theoretical and quantum mechanics in one place and emphasizes the continuity between them. Key topics include:

applications of quantum methods to simple systems, e.g. one-dimensional potential, harmonic oscillator, hydrogen atom, hydrogen-like atoms.

introduction of representation theory and elements of matrix mechanics

development of the perturbation theory

physical explanation of the interaction of an electron with magnetic field

generalization to many-particles systems.

Each chapter includes a detailed outline, a summary, self-assessment questions for which answers are in the text, a varied set of problems. In addition, the book contains many summary tables to ensure clarity of the subject.

This book will be invaluable for chemistry undergraduate and graduate students, chemists, other non-physical scientists, engineering students of modern techniques and technology, specialists who need a better understanding of quantum mechanics. The book is uniquely presented to be used for self-taught courses covering theoretical and quantum mechanics.

 

"I like the approach followed very much. ... He shows clearly that these more advanced and powerful methods can be straightforwardly applied to these problems. His transparant and elegant way of presentation will bring a deeper and more bountiful insight to the student in classical and quantum mechanics..."

Steven Stolte, Department of Chemistry, Vrije Universiteit, The Netherlands.

 "...I think it is a very useful book to have on my bookshelves, especially since it makes a clear connection between classical and quantum mechanics. ...it is very useful for me and theoretically oriented chemists ...I found the book very useful in preparing my lectures for my first-year quantum chemistry course as it gave me more insight into the connection between quantum and classical mechanics. ...'

 Joop van Lenthe, Theoretical Chemistry Group, Utrecht University, The Netherlands.