Problems of Atomic Dynamics

In 1925-26, the future Nobel prize-winner Max Born presented two series of lectures at the Massachusetts Institute of Technology: one on the structure of the atom, the other on the lattice theory of rigid bodies. This volume contains the text of those lectures, during the course of which Born introduced new developments in quantum theory as they occurred: Pauli's fourth quantum number, Dirac's formalism, and elements of his own work on a general operational calculus. Appropriate for upper-level undergraduates and graduate students, Problems of Atomic Dynamics represents a historic view of the foundations of modern quantum theory. 43 figures.

FOREWORD

vii

PREFACE

ix

SERIES I THE STRUCTURE OF THE ATOM

LECTURE 1

1

(11)

Comparison between the classical continuum theory and the quantum theory

Chief experimental results on the structure of the atom

General principles of the quantum theory

Examples.

LECTURE 2

12

(9)

General introduction to mechanics

Canonical equations and canonical transformations.

LECTURE 3

21

(4)

The Hamilton-Jacobi partial differential equation

Action and angle variables

The quantum conditions.

LECTURE 4

25

(7)

Adiabatic invariants

The principle of correspondence.

LECTURE 5

32

(6)

Degenerate systems

Secular perturbations

The quantum integrals.

LECTURE 6

38

(9)

Bohr's theory of the hydrogen atom

Relativity effect and fine structure

Stark and Zeeman effects.

LECTURE 7

47

(7)

Attempts towards a theory of the helium atom and reasons for their failure

Bohr's semi-empirical theory of the structure of higher atoms

The optical electron and the Rydberg-Ritz formula for spectral series

The classification of series

The main quantum numbers of the alkali atoms in the unexcited state.

LECTURE 8

54

(6)

Rohr's principle of successive building of atoms

Arc and spark spectra

X-ray spectra

Rohr's table of the completed numbers of electrons in the stationary states.

LECTURE 9

60

(8)

Sommerfeld's inner quantum numbers

Attempts toward their interpretation by means of the atomic angular momentum

Breakdown of the classical theory

Formal interpretation of spectral regularities

Stoner's definition of subgroups in the periodic system

Pauli's introduction of four quantum numbers for the electron

Pauli's principle of unequal quantum numbers

Report on the development of the formal theory.

LECTURE 10

68

(7)

Introduction to the new quantum theory

Representation of a coordinate by a matrix

The elementary rules of matrix calculus.

LECTURE 11

75

(4)

The commutation rule and its justification by a correspondence consideration

Matrix functions and their differentiation with respect to matrix arguments.

LECTURE 12

79

(4)

The canonical equations of mechanics

Proof of the conservation of energy and of the "frequency condition"

Canonical transformations

The analogue of the Hamilton-Jacobi differential equation.

LECTURE 13

83

(6)

The example of the harmonic oscillator

Perturbation theory.

LECTURE 14

89

(5)

The meaning of external forces in the quantum theory and corresponding perturbation formulas

Their application to the theory of dispersion.

LECTURE 15

94

(5)

Systems of more than one degree of freedom

The commutation rules

The analogue of the Hamilton-Jacobi theory

Degenerate systems.

LECTURE 16

99

(7)

Conservation of angular momentum

Axial symmetrical systems and the quantization of the axial component of angular momentum.

LECTURE 17

106

(7)

Free systems as limiting cases of axially symmetrical systems

Quantization of the total angular momentum

Comparison with the theory of directional quantization

Intensities of the Zeeman components of a spectral line

Remarks on the theory of Zeeman separation.

LECTURE 18

113

(6)

Pauli's theory of the hydrogen atom.

LECTURE 19

119

(6)

Connection with the theory of Hermition forms

Aperiodic motions and continuous spectra.

LECTURE 20

125

(8)

Substitution of the matrix calculus by the general operational calculus for improved treatment of aperiodic motions

Concluding remarks.

SERIES II THE LATTICE THEORY OF RIGID BODIES

LECTURE 1

133

(6)

Classification of crystal properties

Continuum and lattice theories

Geometry of lattices.

LECTURE 2

139

(7)

Molecular forces

Polarizability of atoms

Potential energy and inner forces

Homogeneous displacements

The conditions of equilibrium

Examples of regular lattices.

LECTURE 3

146

(9)

Elimination of inner motions

Compressibility

Elasticity and Hooke's law

Cauchy's relations

Dielectric displacement and piezoelectricity

Residual-ray frequencies.

LECTURE 4

155

(8)

Ionic lattices

Kossel's and Lewis' theory

Calculation of the lattice energy according to Madelung and Ewald.

LECTURE 5

163

(5)

The energy of the rock-salt lattice

Repulsive forces

Derivation of the properties of salt crystals from the properties of inert gases.

LECTURE 6

168

(8)

Experimental determination of the lattice energy by means of cyclic processes

The electron affinity of halogens

Heat of dissociation of salt molecules

Theory of molecular structure.

LECTURE 7

176

(7)

Chemical crystallography

Coordination lattices

Hund's theory of lattice types

Molecule, radical and layer lattices.

LECTURE 8

183

(6)

Physical mineralogy

The parameters of asymmetrical lattices

The molecule lattice of hydrochloric acid

Bragg's calculation of the rhombohedral angle of calcite

Rutile and anatase

Influence of the polarizability on elastic and electric constants

The breaking stress of rock salt.

LECTURE 9

189

(7)

Crystal optics

Refraction and double refraction

Optical activity

Thermodynamics

Quantum theory of specific heats

Distribution of frequencies in phase space.

LECTURE 10

196

Thermal expansion and pyroelectricity

Concluding remarks.

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Problems of Atomic Dynamics

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Table of Contents

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