Quantum mechanics : its early development and the road to entanglement / Edward G. Steward ; with a contribution by Sara M. McMurry.

Format:

Book

Author/Creator:

Steward, E. G. (Edward G.), 1923-

Language:

English

Subjects (All):

Quantum theory.

Mathematical statistics.

Physical Description:

xxi, 257 pages : illustrations ; 23 cm

Place of Publication:

London : Imperial College Press ; Singapore ; Hackensack, NJ : Distributed by World Scientific Pub., [2008]

Summary:

This book provides the reader with an explanation of the origin and establishment of quantum mechanics, with the mathematics in a digestible form, together with a descriptive survey of later developments up to the present day. The mathematical treatment closely follows the original treatment, but in modern terms, using uniform symbolism as much as possible and with simplifications (e.g. the use of one dimension instead of three) to avoid unnecessarily complicated-looking mathematics.

Containing an extensive bibliography and useful appendices as well as references to original works, reviews, and biographies, the reader is well-equipped to delve further into the subject. In addition to its importance for those studying physics, it is also valuable for those studying the history of science.

Contents:

1.2 Light and Heat: Kirchhoff's 'Black-body Radiation' 2

1.3 Kirchhoff's Work on Optical Spectra 4

1.4 Planck's Route to Tackling the Black-body Radiation Problem 5

1.5 Light and the Aether 6

1.6 Post 1900 7

2 Light: The 'Aether' and the Special Theory of Relativity 11

2.2 The 'Aether' 13

2.2.1 The stellar 'aberration of light' 13

2.2.2 Arago's experiments 14

2.2.3 Fresnel's 'drag' mechanism (1818) 15

2.2.4 The 1887 Michelson-Morley experiment 15

2.2.5 The FitzGerald contraction 16

2.2.6 The Lorentz contraction 16

2.3 Einstein's Special Theory of Relativity (1905) 17

2.3.1 Introduction: reference frame transformations 17

2.3.2 Energy and momentum 23

3 Thermal Radiation and Planck's 'Energy Elements' 26

3.2 Planck and 'Energy Elements' 32

3.2.1 Introduction: background 32

3.2.2 Stage 1 34

3.2.3 Stage 2: Planck's final distribution function 39

3.2.4 Summary of the main features of Planck's final derivation of the distribution function 45

4 Einstein and the Quantum 48

4.3 Volume Dependence of Entropy: Light Quanta and the Photoelectric Effect 56

4.4 Fluctuations 62

4.4.1 Energy fluctuations 62

4.4.2 Momentum fluctuations 65

4.5 Statistics: Planck's Radiation Formula and Specific Heat Theory 66

5 The Quantum in the Atom: Optical Spectra 69

5.2 Classical Mechanics of an Electron in a Circular Atomic Orbit 71

5.3 The Quantum is Introduced: The Correspondence Principle 72

6 Einstein's Transition Probabilities: Bohr's Theory and Planck's Law 80

7 Wave Mechanics 85

7.2 de Broglie's Matter Waves 86

7.2.1 Freely moving particles 87

7.2.2 Orbital electrons as waves 91

7.3 Schrodinger's Wave Mechanics 93

7.3.2 Background role of Einstein's Gas Theory 95

7.3.3 Classical wave optics and geometrical optics compared: a note 98

7.3.4 Fermat's principle of least time 99

7.3.5 Maupertuis's principle of least action 101

7.3.6 Hamilton's mechanics and Schrodinger's wave mechanics 103

7.3.7 Schrodinger's time-independent wave equation of 1926 105

7.3.8 Schrodinger's time-dependent equation 112

7.3.9 The probabilistic interpretation of the wave equation 116

7.3.10 Operator representations 119

7.4 Relativistic Wave Equation: The Dirac Equation 120

8 Matrix Mechanics 124

8.2 Heisenberg's Approach 126

8.2.1 Heisenberg invokes the correspondence principle 128

8.2.2 Outside the range of the correspondence principle 130

8.3 The Reconciliation of Matrix Mechanics and Wave Mechanics 132

8.4 Dirac and Matrix Mechanics 133

9 Complementarity, the Uncertainty Principle, and the Copenhagen Interpretation 135

9.2 Heisenberg's Uncertainty Principle 138

9.3 The Como Meeting and the 'Copenhagen Interpretation' 142

9.4 Copenhagen Interpretation Challenged 146

9.4.2 Einstein's objections 150

10 Indeterminacy and Entanglement (Sara M. McMurry) 159

10.2 Entangled Pairs of Particles and Bell's Inequality 161

10.2.1 Photon polarisation and indeterminacy 162

10.2.2 An EPR experiment with photons 166

10.2.3 Hidden variables and Bell's Inequality 168

10.2.4 Experimental tests of Bell's Inequality 172

10.3 Quantum Information Theory 173

10.3.1 Quantum computing 175

10.3.2 Quantum cryptography 176

10.3.3 Quantum cloning and quantum teleportation 177

10.4 The Quantum Measurement Problem 179

10.4.1 Schrodinger's Cat and the collapse of the wave function 180

A Entropy 184

B Classical Thermodynamics; Kinetic Theory; Statistical Mechanics; Statistical Thermodynamics 191

C Phase Space 196

D A Note on Rayleigh's Radiation Formula 204

E Debye: Specific Heat Theory of Solids and Derivation of Planck's Radiation Formula 206

F The Photoelectric Effect 209

G The General Wave Equation; Wave Groups; Dispersion 211

H The Harmonic and Anharmonic Oscillator 214

I Chronology of Main Developments Leading to the Copenhagen Interpretation 219

J Biographical Notes: The Central Characters 223.

Notes:

Includes bibliographical references (pages 231-245) and index.

ISBN:

1860949789

9781860949784

1860949770

9781860949777

OCLC:

191658622