Understanding the Path from Classical to Quantum Mechanics

✍ Scribed by Jaroslav Zamastil

• Tongue: English
• Leaves: 68
• Category: Library

✦ Table of Contents

Preface
Prerequisites
Acknowledgements
Contents
1 Mathematical Preliminaries
1.1 Units
1.2 The Summation Convention
1.3 The Component Formalism
1.4 Dirac δ-function
1.5 Spherical Coordinates
2 Classical Electrodynamics
2.1 Maxwell and Newton Equations
2.2 The Decomposition of the Electromagnetic Field
2.3 Conservation of Energy for a System of N Particles and Electromagnetic Field
2.4 Solution of Maxwell Equations
2.5 Asymptotic Form of Solution
2.6 Emission of Radiation
2.7 Representation of Radiation Damping as Friction
2.8 Dispersion and Absorption of Radiation
2.9 Scattering of Radiation
2.10 Comment on Classical Theory
3 Hamiltonian Formulation of Classical Mechanics
3.1 Hamilton Variational Principle
3.2 Canonical Transformations
3.3 Action–Angle Variables
4 Steps to the Correct Solution
4.1 Empirically Valid Formulae
4.1.1 Planck Radiation Law
4.1.2 Rydberg–Ritz Combination Principle
4.1.3 Balmer Formula for Hydrogen
4.2 Einstein's Derivation of the Planck Radiation Law
4.3 Ladenburg Theory of Dispersion
4.4 Kramers Theory of Dispersion and Its Born's Derivation
4.4.1 Kramers Extension of Ladenburg Formula
4.4.2 Canonical Perturbation Method
4.4.3 Born Quantization Procedure
5 Heisenberg's Magical Steps
5.1 Fourier Series and Its Quantum Reinterpretation
5.2 Multiplication of Two QM Fourier Series
5.3 Equations of Motion
5.4 Quantum Condition
5.5 Existence of a Ground State
5.6 Energy Conservation
5.7 Subsequent Developments
6 Reflections on the Quantum Mechanics and the Path Leading to Its Discovery
References