An Introduction to Quantum Physics

A.P. French

• Publisher: Routledge
• Year: 2018
• ISBN:
  9781351466998
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Physics
• Index: Physics

Provides comprehensive coverage of all the fundamentals of quantum physics. Full mathematical treatments are given. Uses examples from different areas of physics to demonstrate how theories work in practice. Text derived from lectures delivered at Massachusetts Institute of Technology.

1

Simple models of the atom

1-1 INTRODUCTION

We know that classical physics, as represented by Newtonian mechanics and Maxwell’s laws of electromagnetism, works marvelously well for the analysis of the behavior of macroscopic objects in terms of empirically determined laws of force. But as soon as we enter the world of the atom, we find that new phenomena appear, requiring new concepts for their analysis and description. The whole realm of phenomena at the atomic or subatomic level is the special province of quantum theory. However, because the behavior of matter in bulk ultimately results from the properties of its constituent atoms, our deeper insights into physical phenomena on the macroscopic scale will often also depend on quantum theory. For example: We can do a vast amount of useful analysis of the mechanical behavior of solids using measured values of their elastic constants, tensile strengths, etc. But if we want to account for these measured values in terms of more fundamental processes, we must invoke quantum theory. It is at the root of our whole understanding of the structure of matter.

The properties of atoms—and even the fact of their existence—pose a series of questions unanswerable by classical physics:

Atoms are typically a few angstroms in diameter (1Å = 10⁻⁸ cm) with remarkably little difference in size between the lightest and the heaviest (see Figure 1-1).

Fig. 1-1 Atomic radii. There is very little increase in atomic size with increasing atomic mass number. Note the periodic variation in radius, with the maximum radii being those of the alkali atoms.

Why this size rather than some other? And why not a wide range of sizes?

When isolated from radiation and other atoms, most atoms remain stable indefinitely: they neither collapse nor explode. Why do not the negatively charged electrons collapse into the positively charged nucleus, thereby destroying the atom to the accompaniment of a burst of radiation?

When atoms are excited electrically or by collisions or otherwise, they emit radiation of discrete wavelengths characteristic of the kind of atoms excited (see Figure 1-2). Why discrete wavelengths rather than a continuous spectrum? And how can a particular spectrum be accounted for, as well as differences between spectra of different kinds of atoms?

Fig. 1-2 Emission spectra of various vapors. The pattern of emission lines in each spectrum is characteristic of the particular chemical element. (Spectra reproduced from G. Herzberg, Atomic Spectra and Atomic Structure, Dover Publications, Inc., New York, 1944. Reprinted through the permission of the publisher.)

These questions are only a beginning. Why are some kinds of atoms more reactive chemically than other kinds? Why are some substances harder, denser, more transparent, more elastic, more electrically conductive, more thermally conductive, more digestible than other substances? All such questions can be related to the properties of atoms, and we can understand them only if we possess the facts and concepts embodied in quantum mechanics.

In this book we will turn our attention again and again to the atom, each time from a different point of view or level of sophistication. In the present chapter we discuss a few of the simplest models of the atom, all of them basically classical in nature, with one or two additional assumptions to help the classical models behave more like the observed quantum systems. Despite their crude nature these models can be used to correlate, even if they cannot be said to explain, a wide range of observations. The ultimate failures of these models force us to look more deeply and to return repeatedly to the atom with models of increasing sophistication.

Why start with crude models? Why return again and again to them when the “real” answers are already known?

Why not tell the quantum-mechanical truth straight out and then stop? Some readers may feel equipped to go straight to the now-accepted answers, and they can begin their study with a later chapter of this text. But for most people crude atomic models provide a gradual conceptual transition from classical descriptions to the “true” quantum statements about atoms, statements that seem strange and awkward at first but later on become comfortable, simple, and natural.

1-2 THE CLASSICAL ATOM¹

The simplest model of the atom is a hard, tiny, electrically neutral sphere—just the smallest possible fragment of the bulk material that still possesses the identity of a given chemical element. According to this conceptually primitive picture, atoms (and molecules formed from them) exert no forces on one another until they are brought in contact, and then they offer infinite resistance to being forced any closer together. The dramatic difference in behavior between a substance in vapor form, on the one hand, and in its solid or liquid phase, on the other, is roughly consistent with such a model. This major difference in behavior does not involve a big change in interatomic or intermolec...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• PREFACE
• LEARNING AIDS FOR QUANTUM PHYSICS
• 1 Simple models of the atom
• 2 The wave properties of particles
• 3 Wave-particle duality and bound states
• 4 Solutions of Schrodinger’s equation in one dimension
• 5 Further applications of Schrodinger’s equation
• 6 Photons and quantum states
• 7 Quantum amplitudes and state vectors
• 8 The time dependence of quantum states
• 9 Particle scattering and barrier penetration
• 10 Angular momentum
• 11 Angular momentum of atomic systems
• 12 Quantum states of three-dimensional systems
• 13 Identical particles and atomic structure
• 14 Radiation by atoms
• ANSWERS TO EXERCISES
• BIBLIOGRAPHY
• SELECTED PHYSICAL CONSTANTS AND CONVERSION FACTORS
• INDEX