Basic Molecular Quantum Mechanics

Steven A. Adelman

• Publisher: CRC Press
• Year: 2021
• Print ISBN: 9781032010656
• eBook ISBN: 9781498734066
• Topic: Physical Sciences
• Subtopic: Chemistry
• Index: Chemistry

Quantum mechanics is a general theory of the motions, structures, properties, and behaviors of particles of atomic and subatomic dimensions. While quantum mechanics was created in the first third of the twentieth century by a handful of theoretical physicists working on a limited number of problems, it has further developed and is now applied by a great number of people working on a vast range of problems in wide areas of science and technology.

Basic Molecular Quantum Mechanics introduces quantum mechanics by covering the fundamentals of quantum mechanics and some of its most important chemical applications: vibrational and rotational spectroscopy and electronic structure of atoms and molecules. Thoughtfully organized, the author builds up quantum mechanics systematically with each chapter preparing the student for the more advanced chapters and complex applications. Additional features include the following:

• This book presents rigorous and precise explanations of quantum mechanics and mathematical proofs.
• It contains qualitative discussions of key concepts with mathematics presented in the appendices.
• It provides problems and solutions at the end of each chapter to encourage understanding and application.

This book is carefully written to emphasize its applications to chemistry and is a valuable resource for advanced undergraduates and beginning graduate students specializing in chemistry, in related fields such as chemical engineering and materials science, and in some areas of biology.

1 Toward Quantum Mechanics

Classical mechanics introduced in Appendix A is the theory of motion developed by Isaac Newton in the last third of the seventeenth century. Classical mechanics successfully describes a tremendous range of phenomena. A few examples include the “break” of a curveball thrown by a major league pitcher, the orbiting of a planet about the sun, the propagation of tidal waves, the vibrations of a violin string, the flow of fluids, and the transmission of sound.

However, by the end of the nineteenth century, experimental results had emerged which revealed phenomena outside of the purview of both classical mechanics and one of the two other pillars of nineteenth-century physics (the second being thermodynamics) Maxwell’s theory of the electromagnetic field. From the theoretical analyses of these phenomena and additional phenomena discovered in the early part of the twentieth century as well as from purely theoretical considerations, it eventually became clear that classical mechanics failed when applied to very small particles such as atoms, molecules, and electrons and that a new form of mechanics, quantum mechanics, was needed to study the motions of such particles.

The development of quantum mechanics required a radical revision of many of the most basic principles of physics and so it only very gradually emerged over the thirty-year period, ~1900–1930. In this chapter, we describe the first stages of this emergence. We particularly introduce the new ideas that permitted the explanation of four classically inexplicable phenomena: (a) the blackbody radiation spectrum, (b) the photoelectric effect, (c) the low-temperature heat capacities of solids, and most importantly, (d) the line spectra of the hydrogen atom.

We begin by describing how Planck and Einstein explained the first three of these phenomena by introducing the revolutionary concept of energy quanta.

1.1 Energy Quanta

We start with blackbody radiation.

To begin, we note that a chunk of metal or any other body continually emits electromagnetic radiation or light. At room temperature, most of this light lies in the infrared region of the electromagnetic spectrum and thus is invisible. But if the chunk ...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Preface
• Acknowledgments
• Author
• Chapter 1 Toward Quantum Mechanics
• Chapter 2 Mathematics for Quantum Mechanics
• Chapter 3 The Schrödinger Equation and the Particle-in-a-Box
• Chapter 4 Wave Functions and Experimental Outcomes
• Chapter 5 Commutation Rules and Uncertainty Relations
• Chapter 6 Stationary and Non-stationary Quantum States
• Chapter 7 The Harmonic Oscillator
• Chapter 8 Rigid Rotations and Rotational Angular Momentum
• Chapter 9 Diatomic Rotational–Vibrational Spectroscopy
• Chapter 10 The Hydrogen-Like Atoms
• Chapter 11 Approximation Methods
• Chapter 12 Electrons in Atoms
• Chapter 13 Molecular Electronic Structure and Chemical Bonding
• Appendix A: Elements of Classical Dynamics
• Appendix B: Classical Theory of Diatomic Rotational–Vibrational Motions
• Appendix C: Solution of the Time-Independent Schrödinger Equation for the One-Dimensional Harmonic Oscillator
• Appendix D: Solution of the Radial Schrödinger Equation for Hydrogen-Like Atoms
• Index