Introduction to Quantum Mechanics with Applications to Chemistry

Linus Pauling, E. Bright Wilson, E. Bright Wilson

• Publisher: Dover Publications
• Year: 2012
• Print ISBN: 9780486648712
• eBook ISBN: 9780486134932
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

When this classic text was first published in 1935, it fulfilled the goal of its authors "to produce a textbook of practical quantum mechanics for the chemist, the experimental physicist, and the beginning student of theoretical physics." Although many who are teachers today once worked with the book as students, the text is still as valuable for the same undergraduate audience.
Two-time Nobel Prize winner Linus Pauling, Research Professor at the Linus Pauling Institute of Science and Medicine, Palo Alto, California, and E. Bright Wilson, Jr., Professor Emeritus of Chemistry at Harvard University, provide a readily understandable study of "wave mechanics," discussing the Schrodinger wave equation and the problems which can be solved with it. Extensive knowledge of mathematics is not required, although the student must have a grasp of elementary mathematics through the calculus. Pauling and Wilson begin with a survey of classical mechanics, including Newton's equations of motion in the Lagrangian form, and then move on to the "old" quantum theory, developed through the work of Planck, Einstein and Bohr. This analysis leads to the heart of the book ― an explanation of quantum mechanics which, as Schrodinger formulated it, "involves the renunciation of the hope of describing in exact detail the behavior of a system." Physics had created a new realm in which classical, Newtonian certainties were replaced by probabilities ― a change which Heisenberg's uncertainty principle (described in this book) subsequently reinforced.
With clarity and precision, the authors guide the student from topic to topic, covering such subjects as the wave functions for the hydrogen atom, perturbation theory, the Pauli exclusion principle, the structure of simple and complex molecules, Van der Waals forces, and systems in thermodynamic equilibrium. To insure that the student can follow the mathematical derivations, Pauling and Wilson avoid the "temptation to condense the various discussions into shorter and perhaps more elegant forms" appropriate for a more advanced audience. Introduction to Quantum Mechanics is a perfect vehicle for demonstrating the practical application of quantum mechanics to a broad spectrum of chemical and physical problems.

INTRODUCTION TO QUANTUM MECHANICS

CHAPTER I

SURVEY OF CLASSICAL MECHANICS

The subject of quantum mechanics constitutes the most recent step in the very old search for the general laws governing the motion of matter. For a long time investigators confined their efforts to studying the dynamics of bodies of macroscopic dimensions, and while the science of mechanics remained in that stage it was properly considered a branch of physics. Since the development of atomic theory there has been a change of emphasis. It was recognized that the older laws are not correct when applied to atoms and electrons, without considerable modification. Moreover, the success which has been obtained in making the necessary modifications of the older laws has also had the result of depriving physics of sole claim upon them, since it is now realized that the combining power of atoms and, in fact, all the chemical properties of atoms and molecules are explicable in terms of the laws governing the motions of the electrons and nuclei composing them.

Although it is the modern theory of quantum mechanics in which we are primarily interested because of its applications to chemical problems, it is desirable for us first to discuss briefly the background of classical mechanics from which it was developed. By so doing we not only follow to a certain extent the historical development, but we also introduce in a more familiar form many concepts which are retained in the later theory. We shall also treat certain problems in the first few chapters by the methods of the older theories in preparation for their later treatment by quantum mechanics. It is for this reason that the student is advised to consider the exercises of the first few chapters carefully and to retain for later reference the results which are secured.

In the first chapter no attempt will be made to give any parts of classical dynamics but those which are useful in the treatment of atomic and molecular problems. With this restriction, we have felt justified in omitting discussion of the dynamics of rigid bodies, non-conservative systems, non-holonomic systems, systems involving impact, etc. Moreover, no use is made of Hamilton's principle or of the Hamilton-Jacobi partial differential equation. By thus limiting the subjects to be discussed, it is possible to give in a short chapter a thorough treatment of Newtonian systems of point particles.

1. NEWTON'S EQUATIONS OF MOTION IN THE LAGRANGIAN FORM

The earliest formulation of dynamical laws of wide application is that of Sir Isaac Newton. If we adopt the notation x_i, y_i, z_i for the three Cartesian coordinates of the i′th particle with mass m_i, Newton's equations for n point particles are

where X_i, Y_i, Z_i are the three components of the force acting on the ith particle. There is a set of such equations for each particle. Dots refer to differentiation with respect to time, so that

By introducing certain familiar definitions we change Equation 1–1 into a form which will be more useful later. We define as the kinetic energy T (for Cartesian coordinates) the quantity

If we limit...

Table of contents

• Cover
• Title Page
• Copyright Page
• Preface
• Contents
• Chapter I: Survey of Classical Mechanics
• Chapter II: The Old Quantum Theory
• Chapter III: The Schrödinger Wave Equation with the Harmonic Oscillator as an Example
• Chapter IV: The Wave Equation for a System of Point Particles in Three Dimensions
• Chapter V: The Hydrogen Atom
• Chapter VI: Perturbation Theory
• Chapter VII: The Variation Method and other Approximate Methods
• Chapter VIII: The Spinning Electron and the Pauli Exclusion Principle, with a Discussion of the Helium Atom
• Chapter IX: Many-Electron Atoms
• Chapter X: The Rotation and Vibration of Molecules
• Chapter XI: Perturbation Theory Involving the Time, the Emission and Absorption of Radiation, and the Resonance Phenomenon
• Chapter XII: The Structure of Simple Molecules
• Chapter XIII: The Structure of Complex Molecules
• Chapter XIV: Miscellaneous Applications of Quantum Mechanics
• Chapter XV: General Theory of Quantum Mechanics
• Appendix I: Values of Physical Constants
• Appendix II: Proof that the Orbit of a Particle Moving in a Central Field Lies in a Plane
• Appendix III: Proof of Orthogonality of Wave Functions Corresponding to Different Energy Levels
• Appendix IV: Orthogonal Curvilinear Coordinate Systems
• Appendix V: The Evaluation of the Mutual Electrostatic Energy of Two Spherically Symmetrical Distributions of Electricity with Exponential Density Functions
• Appendix VI: Normalization of the Associated Legendre Functions
• Appendix VII: Normalization of the Associated Laguerre Functions
• Appendix VIII: The Greek Alphabet
• Index