Author: "Peter Enders"

Classical Mechanics and Quantum Mechanics: An Historic-Axiomatic Approach

eBook: US $49 Special Offer (PDF + Printed Copy): US $148
Printed Copy: US $124
Library License: US $196
ISBN: 978-1-68108-450-3
eISBN: 978-1-68108-449-7 (Online)
DOI: 10.2174/97816810844971190101
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Introduction

This unique textbook presents a novel, axiomatic pedagogical path from classical to quantum physics. Readers are introduced to the description of classical mechanics, which rests on Euler’s and Helmholtz’s rather than Newton’s or Hamilton’s representations. Special attention is given to the common attributes rather than to the differences between classical and quantum mechanics. Readers will also learn about Schrödinger’s forgotten demands on quantization, his equation, Einstein’s idea of ‘quantization as selection problem’. The Schrödinger equation is derived without any assumptions about the nature of quantum systems, such as interference and superposition, or the existence of a quantum of action, h. The use of the classical expressions for the potential and kinetic energies within quantum physics is justified.

Key features:

This book addresses the needs of physics students, teachers and historians with its simple easy to understand presentation and comprehensive approach to both classical and quantum mechanics.

Foreword

- Pp. i-ii (2)
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Preface

- Pp. iii-xi (9)
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Introduction

- Pp. 1-19 (19)
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Newton-Eulerian Axiomatic: The Notion of State

- Pp. 21-58 (38)
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Alternative Axiomatic: Energy Conservation

- Pp. 59-73 (15)
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Possible and Impossible (Momentum) Configurations

- Pp. 74-77 (4)
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Why Quantum Mechanics?

- Pp. 79-88 (10)
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A Hierarchy of Selection Problems

- Pp. 89-96 (8)
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Non-Classical Representations of Potential, Kinetic and Total Energies

- Pp. 97-103 (7)
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Conservation of Stationary Quantum States Stationary Schrödinger Equation

- Pp. 104-109 (6)
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Non-Classical Selection of the Physical Solutions

- Pp. 110-127 (18)
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Additional Results

- Pp. 128-140 (13)
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Conservation and Change of Stationary States

- Pp. 142-150 (9)
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Equation of Motion

- Pp. 151-158 (8)
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Conservation Laws

- Pp. 159-165 (7)
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Applications

- Pp. 166-175 (10)
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General Considerations

- Pp. 176-178 (3)
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Space-time Symmetries

- Pp. 179-198 (20)
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Gauge Symmetry

- Pp. 199-212 (14)
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Permutation Symmetry

- Pp. 213-224 (12)
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‘Aequat Causa Effectum’ Spherically Symmetric Potentials versus Non-spherically Symmetric Orbits and Orbitals

- Pp. 225-244 (20)
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Introduction

- Pp. 245-246 (2)
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Coupled Classical Oscillators

- Pp. 247-250 (4)
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From Chains to Strings: Limit Transition to the Continuum

- Pp. 251-255 (5)
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Quantization of the String

- Pp. 256-260 (5)
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Quantization of the Free Electromagnetic Field

- Pp. 261-268 (8)
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Summary and Conclusions

- Pp. 271-280 (10)
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Open Questions – Suggestions

- Pp. 281-284 (4)
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Points of Extension or Generalization

- Pp. 285-292 (8)
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References And Further Reading

- Pp. 293-346 (54)
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Subject Index

- Pp. 347-351 (5)
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