Author: "Peter Enders"

Classical Mechanics and Quantum Mechanics: An Historic-Axiomatic Approach

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

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:

  • - Presents extensive reference to original texts.
  • - Includes many details that do not enter contemporary representations of classical mechanics, although these details are essential for understanding quantum physics.
  • - Contains a simple level of mathematics which is seldom higher than that of the common (Riemannian) integral.
  • - Brings information about important scientists
  • - Carefully introduces basic equations, notations and quantities in simple steps

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

This is not just another textbook about quantum mechanics as it presents quite a novel, axiomatic path from classical to quantum physics. The novelty begins with the description of classical mechanics, which rests on Euler’s and Helmholtz’s rather than Newton’s or Hamilton’s representations. Special attention is paid to the commons rather than to the differences between classical and quantum mechanics. Schrödinger’s 1926 forgotten demands on quantization are taken seriously; therefore, his paradigm ‘quantization as eigenvalue problem’ is replaced with 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.

A doubtless benefit of this textbook is its extensive reference to original texts. This includes many details that do not enter contemporary representations of classical mechanics, although these details are essential for understanding quantum physics.

Another benefit consists in that it addresses not only students and scientists, but also teachers and historians; it sheds new light on the history of ideas and notions. The level of mathematics is seldom higher than that of the common (Riemannian) integral. Basic notions and quantities are carefully introduced; steps like “It can be shown, that textellipsis…” or ‘It’s sink or swim’ are successfully avoided.

“From Newton to Planck and even more. The mix of exacting physics, biography and history exhibits its quite own charm and quickly fascinates the reader – in particular, when nowadays physical equations and the historical literature are so masterly interwoven as the paramount historical figures with their epochal works.” (Carsten Hansen, review on buchkatalog.de)

“I would like to express my thank to the author for this book. It contains an impressive and comprehensible derivation and representation of quantum physics. Due to his approach, I have eventually found an approach that is acceptable for me and not purely formal. The way from classical to quantum physics is impressively understood. Using a profound knowledge of the historical literature, including the original texts, the Schroedinger equation is derived through an extension of Euler’s and Helmholtz’s representations of classical mechanics to non-classical systems. It is the concentration on the commons rather than on the differences between classical and quantum systems that makes this approach reasonable. Moreover, this makes the interpretation and meaningfulness of the quantum-mechanical models and concepts clearly visible.”


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