Stringer / Owen / Hopkins An Introduction to the Electron Theory of Solids

Metallurgy Division
1. Auflage 2013
ISBN: 978-1-4831-3671-4
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 256 Seiten, Web PDF

An Introduction to the Electron Theory of Solids introduces the reader to the electron theory of solids. Topics covered range from the breakdown of classical theory to atomic spectra and the old quantum theory, as well as the uncertainty principle of Heisenberg and the foundations of quantum mechanics. Some problems in wave mechanics and a wave-mechanical treatment of the simple harmonic oscillator and the hydrogen atom are also presented. Comprised of 12 chapters, this book begins with an introduction to Isaac Newton's theory of classical mechanics and how the scientists after him discounted his ideas. The discussion then turns to the spectrum of atomic hydrogen and the old quantum theory; Heisenberg's uncertainty principle and the consequences of wave-particle duality; the foundations of quantum mechanics; and assemblies of atoms. Atoms in motion and statistical mechanics are also considered, along with simple models of metals and the band theory of solids. The final chapter presents some results of band theory, with particular reference to thermal ionization of impurity atoms and conductivity of metals. This monograph is primarily intended for students of any discipline.

Autoren/Hrsg.

Stringer, John

Owen, W. S.

Hopkins, D. W.

Finniston, H. M.

Inhaltsverzeichnis

1;Front Cover;1
2;An Introduction to the Electron Theory of Solids;4
3;Copyright Page;5
4;Table of Contents;6
5;Introduction;8
6;Chapter 1. The Breakdown of Classical Theory;12
6.1;Particles versus Waves;12
6.2;The Photoelectric Effect;15
6.3;How Big is a Photon?;19
6.4;Wave–Particle Duality;20
6.5;The Particle Character of the Electron;22
7;Chapter 2. Atomic Spectra and the Old Quantum Theory;24
7.1;The Spectrum of Atomic Hydrogen;24
7.2;The Old Quantum Theory;27
7.3;Sommerfeld's Modification;35
7.4;The Third Degree of Freedom—the Zeeman Effect;38
7.5;The Spectra of the Alkali Metals: Spin;41
7.6;The Pauli Exclusion Principle;43
7.7;Conclusions;44
8;Chapter 3. The Uncertainty Principle of Heisenberg;45
8.1;The Consequences of Wave–Particle Duality;45
8.2;Bohr's Microscope Experiment;51
8.3;Phase Velocity and Group Velocity;54
9;Chapter 4. The Foundations of Quantum Mechanics;58
9.1;Wave Mechanics and Matrix Mechanics;58
9.2;The First Postulate of Wave Mechanics: The Wave Equation;59
9.3;The Wave Equation;59
9.4;Eigenfunctions and Eigenvalues;64
9.5;The Second Postulate of Wave Mechanics;65
9.6;Generalisation to Three Dimensions;67
9.7;The Significance of the Wave Function;68
10;Chapter 5. Some Problems in Wave Mechanics;70
10.1;A Free Particle Moving in One Dimension;70
10.2;A Particle Travelling in One Dimension Incident on a Potential Barrier;71
10.3;The Tunnel Effect;77
10.4;A Particle in a Potential Box;80
10.5;Three-dimensional Potential Box;82
10.6;Many-particle Systems and the Pauli Exclusion Principle;85
11;Chapter 6. A Wave-Mechanical Treatment of the Simple Harmonic Oscillator and the Hydrogen Atom;90
11.1;The Simple Harmonic Oscillator;90
11.2;A Particle in a Coulomb Field: the Hydrogen Atom;95
11.3;The Labelling of States and the Periodic Table;102
11.4;Spin and Wave Mechanics;111
12;Chapter 7. Assemblies of atoms;112
12.1;The Hydrogen Molecular Ion H2 +;112
12.2;The Hydrogen Molecule H2;120
12.3;Directionality of Bonding;128
12.4;Forces Between Neutral Atoms and Molecules;129
12.5;Bonding Between Unlike Atoms;134
12.6;The Hydrogen Bridge;136
12.7;The Metallic Bond;136
13;Chapter 8. Atoms in Motion;138
13.1;The Potential Energy of a System of Molecules;141
13.2;Propagation of an Elastic Wave;144
13.3;Wave Motion of a Line of Similar Atoms;146
13.4;Quantum Restrictions;160
13.5;Calculation of Thermal Conductivity;161
14;Chapter 9. Statistical Mechanics;164
14.1;The Basic Problem;165
14.2;Quantum Statistics;171
14.3;The Specific Heat of a Maxwell–Boltzmann Gas;174
14.4;The Effect of the Pauli Exclusion Principle;175
14.5;The Fermi-Dirac Distribution Function;177
14.6;Integration of the Fermi–Dirac Distribution Function at Absolute Zero;179
14.7;The Temperature Variation of the Fermi Energy at Low Temperatures;180
14.8;The Total Energy of a Degenerate Fermion Gas;183
14.9;The Specific Heat of a Degenerate Fermion Gas;184
15;Chapter 10. Simple Models of Metals;186
15.1;Some Useful Results of the Kinetic Theory of Gases;187
15.2;Conduction of Electricity by a Drude Metal;191
15.3;The Conduction of Heat by a Drude Metal;195
15.4;The Specific Heat of a Drude Metal;198
15.5;Lorentz's Modification of the Drude Model;199
15.6;Sommerfeld's Model of a Metal;200
15.7;Quantitative Treatment of the Sommerfeld Model;202
15.8;Relaxation in the Sommerfeld Model;203
16;Chapter 11. The Band Theory of Solids;206
16.1;Variation of Band Spectrum with Atomic Spacing;208
16.2;Electrical Properties of Solids in Terms of Band Theory;210
16.3;Impurity Semiconductors;217
16.4;A Summary of the Band Theory;223
16.5;Nearly Free Electron Theory;223
16.6;The Concept of Effective Mass;228
16.7;Energy Contours in the Brillouin Zone;231
16.8;Density of States Functions in Band Theory;235
17;Chapter 12. Some Results of Band Theory;240
17.1;Thermal Ionisation of Impurity Atoms;244
17.2;Conductivity of Metals;248
18;Index;254