The historical and physical foundations of quantum mechanics / Robert Golub, Steve Lamoreaux.

Format:

Book

Author/Creator:

Golub, Robert, author.

Lamoreaux, Steve, author.

Language:

English

Subjects (All):

Quantum theory--History.

Quantum theory.

Genre:

History.

Physical Description:

1 online resource (769 pages)

Place of Publication:

Oxford, England : Oxford University Press, [2023]

Summary:

Placing the development of quantum mechanics in its historical context, from its philosophical origins in Greece, to its scientific realisation in the 19th and 20th centuries, this textbook book culminates with an examination of the current state of the field and an introduction to quantum information and computing.

Contents:

cover

titlepage

copyright

dedication

preface

Acknowledgements

contents

PART I Basis of the Theory

1 Introduction

1.1 Overview

1.2 The Prehistory of Quantum Mechanics: atomism

1.3 Religion and science

1.4 Birth of the modern atomic theory of matter

1.5 Atomism and physics

1.5.1 Atomism and anti-atomism: the emergence of atomic physics

2 Properties of the quantum world: indeterminacy, interference, superposition, entanglement

2.1 Indeterminacy-random behavior

2.2 The wave nature of light and matter and its connection with random behavior

2.2.1 Photons

2.2.2 Electrons

2.3 Superposition and projection

2.3.1 Linearly polarized light

2.3.2 Circularly polarized light: an alternative description

2.3.3 Photons

2.4 Entanglement-``spooky action at a distance

2.5 The Aharonov-Bohm effect and the physical reality of electromagnetic potentials

2.6 Quantum mechanics and precision measurements

2.7 Synopsis

3 The origin of quantum theory in the crisis of classical physics

3.1 Black body radiation

3.1.1 Progress before Planck

3.1.2 Planck and Wien's law

3.1.3 The failure of Wien's law and Planck's expression for the black body spectrum

3.1.4 An ``act of desperation''-the introduction of the quantum

3.1.5 Lord Rayleigh derives the Rayleigh-Jeans law

3.2 Einstein further develops the quantum idea

3.2.1 Quantization of the radiation field

3.2.2 The photoelectric effect

3.2.3 A new derivation of the Planck spectrum

3.2.4 A derivation of Planck's law based on interactions between atoms and radiation

3.2.5 Fluctuations and the quantization of the energy of the radiation field

3.2.6 Photons carry momentum as well as energy

3.2.7 Summary of Einstein's work on photons, 1905-1917

3.3 The Bohr atom

3.4 Conclusion.

4 Further steps to quantum mechanics: the old quantum mechanics of Bohr and Sommerfeld

4.1 Quantization conditions

4.2 ``Old'' quantum theory

4.2.1 Quantization of elliptic orbits in the hydrogen atom

4.2.2 Spatial quantization

4.2.3 Fine structure of the hydrogen lines

4.2.4 The Bohr correspondence principle

4.3 Toward quantum mechanics: classical mechanics as the limit of a wave motion

4.4 Conclusion

5 Further steps to quantum mechanics: Louis de Broglie and the world's most important PhD thesis

5.1 Introduction

5.2 De Broglie's contribution

5.2.1 Particles accompanied by oscillatory phenomena

5.2.2 Relation between the ``phase wave'' and particle motion

5.2.3 The Bohr-Sommerfeld quantum conditions

5.2.4 Quantization of phase space

5.2.5 De Broglie's ideas on the relation between the phase wave and the particle motion

5.3 Appendix to Chapter 5-Compton scattering

6 The invention of quantum mechanics-matrix mechanics

6.1 Introduction

6.2 Heisenberg rediscovers matrices

6.3 The founding of matrix mechanics by Born, Jordan, and Heisenberg

6.3.1 The simple harmonic oscillator

6.3.2 Canonical transformations and perturbation theory

6.4 Further developments

6.5 Conclusion

7 Schrödinger and the development of wave mechanics

7.1 Ideas leading to wave mechanics

7.1.1 Introduction

7.1.2 First glimmers of a relationship between phase and the quantum condition

7.1.3 The relationship between particles and waves in the quantum theory of the monatomic ideal gas

7.1.4 First appearance of a wave equation

7.1.5 "Quantization as an eigenvalue problem"

7.1.6 Peter Debye

7.1.7 Summary of Schrödinger's work leading to the wave equation

7.2 The development of wave mechanics as presented in Schrödinger's publications.

7.2.1 Derivation of the wave equation from a variational principle

7.2.2 Applications of the variational principle

7.2.3 Derivation of the wave equation using Hamilton's analogy between point mechanics and geometric optics

7.3 First applications of the wave equation

7.3.1 The harmonic oscillator

7.3.2 Square well potential box

7.3.3 Rigid rotor with a free axis

7.3.4 The hydrogen atom

7.4 The relation between matrix and wave mechanics

7.4.1 First speculations on the emission of radiation according to wave mechanics

7.4.2 Relation to integral equations

8 Further developments of wave mechanics by Schrödinger

8.1 Introduction

8.2 Perturbation theory

8.3 The time-dependent Schrödinger equation

8.3.1 Time-dependent perturbation theory: interaction of light with an atom

8.3.2 First discussion of the physical meaning of the wave function

8.3.3 Modern treatment of time-dependent perturbation theory

8.4 Conclusion

9 Quantum statistics and the origin of wave mechanics

9.1 Bose-Einstein statistics

9.1.1 Introduction

9.1.2 Planck

9.1.3 Bose

9.1.4 Einstein

9.1.5 Schrödinger

9.1.6 Summary

9.2 Fermi-Dirac statistics

9.2.1 Introduction

9.2.2 The physics of multi-electron atoms and the Pauli exclusion principle

9.2.3 Fermi

9.2.4 Dirac

9.2.5 Early applications of Fermi-Dirac statistics

9.3 Conclusion

10 Early attempts at interpretation of the theory

10.1 Introduction

10.2 Schrödinger and the spreading of wave packets

10.2.1 Wave packets for a particle in a box

10.3 Born's insight and the loss of determinacy in physics

10.3.1 Elastic scattering of a particle by an atom

10.3.2 Inelastic scattering of a particle by a fixed atom

10.3.3 Born's interpretation of the wave function

10.4 Heisenberg's uncertainty principle.

10.4.1 The minimum uncertainty wave packet

10.4.2 Spreading of the minimum uncertainty wave packet

10.4.3 Heisenberg's interpretation of quantum mechanics as presented in his 1927 paper ``On the intuitive content of the quantum theoretical kinematics and mechanics

10.5 Niels Bohr and complementarity: the Copenhagen interpretation of quantum mechanics

10.6 Conflicting views on quantum jumps

10.6.1 The Compton effect as a wave phenomenon

10.6.2 Transitions without quantum jumps

10.7 Chronology of Bohr-Heisenberg-Schrödinger discussions

11 The final synthesis of quantum mechanics: the ``transformation theory'' and Dirac notation

11.1 Introduction

11.2 Sturm-Liouville theory, Hilbert space, and linear operators

11.2.1 The Sturm-Liouville operator is self-adjoint

11.2.2 The eigenvalues are real

11.2.3 The eigenfunctions are orthogonal

11.2.4 The eigenvalues form an ascending series

11.2.5 The eigenfunctions form a complete set

11.2.6 Delta function and completeness

11.2.7 Applications to quantum mechanics via the Schrödinger equation

11.3 Dirac's bra-ket notation

11.3.1 Operators

11.3.2 Continuous spectra

11.3.3 Momentum space wave functions

11.4 General features of the theory and Dirac notation

11.4.1 The rules of quantum mechanics

12 Dirac and Jordan commit ``sin squared'': second quantization and the beginning of quantum field theory

12.1 Introduction

12.2 Dirac's q-numbers, operators, and the quantum mechanics of Dirac, Jordan, and von Neumann

12.2.1 Some additional properties of noncommuting operators

12.2.2 Solution of the one dimensional harmonic oscillator by the operator method

12.3 The beginning of quantum field theory

12.3.1 The vibrating string as an example of a continuous field with an infinite number of degrees of freedom.

12.3.2 Dirac shows how to quantize the electromagnetic field

12.3.3 The width of spectral lines: the Weisskopf-Wigner theory

12.3.4 Discussion: wave-particle duality

12.3.5 Following Dirac, Jordan commits ``sin squared'' on his own

12.4 Ehrenfest's theorem and the classical limit of quantum mechanics

12.5 Stability of matter-second quantization

13 The "completion of quantum mechanics"-the fifth Solvay Conference on Physics, October 1927

13.1 Introduction

13.2 The collapse of the wave function and its meaning-the measurement problem

13.2.1 Born and Heisenberg's discussion of superposition

13.2.2 Wave function collapse as seen by Dirac and Heisenberg

13.3 Wave-particle duality

13.3.1 Bohr and complementarity

13.3.2 De Broglie's proposal of a pilot wave

13.4 Einstein and Bohr: the battle of the century?

13.4.1 Einstein's contribution to the published discussions

13.4.2 Einstein and Bohr: off the record discussions

13.4.3 Quantitative approach to Bohr's argument concerning two-slit interference

13.5 The question of 3N dimensions

13.6 Conclusion

14 Von Neumann's mathematical foundations of quantum mechanics: redux

14.1 Introduction

14.2 Von Neumann's measurement theory

14.3 No hidden parameters proof

14.3.1 Implications of hidden variables

14.3.2 ``Dispersion-free'' states and homogeneous ensembles in quantum mechanics

14.3.3 No hidden variables ``theorem

14.4 Von Neumann entropy

14.5 Conclusion

15 Einstein and Schrödinger renew the assault on quantum mechanics

15.1 Introduction

15.2 Einstein attacks quantum theory

15.2.1 Elaborations and modern representations of the EPR problem

15.3 Reactions to the Einstein Podolsky Rosen (EPR) argument

15.3.1 Pauli

15.3.2 Heisenberg

15.3.3 Bohr

15.3.4 Schrödinger

15.3.5 Furry

15.3.6 Schrödinger's cat.

15.3.7 Einstein.

Notes:

Description based on print version record.

Includes index.

ISBN:

0-19-255536-7