Free Direct Download Advanced Quantum Mechanics BY Peter S. Riseborough
Release Date : February 19 2015
Contents
1 Introduction 5
2 Quantum Mechanics of a Single Photon 6
2.1 Rotations and Intrinsic Spin . . . . . . . . . . . . . . . . . . . . . 7
2.2 Massless Particles with Spin Zero . . . . . . . . . . . . . . . . . . 11
2.3 Massless Particles with Spin One . . . . . . . . . . . . . . . . . . 12
3 Maxwell’s Equations 14
3.1 Vector and Scalar Potentials . . . . . . . . . . . . . . . . . . . . . 15
3.2 Gauge Invariance . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4 Relativistic Formulation of Electrodynamics 20
4.1 Lorentz Scalars and Vectors . . . . . . . . . . . . . . . . . . . . . 20
4.2 Covariant and Contravariant Derivatives . . . . . . . . . . . . . . 22
4.3 Lorentz Transformations . . . . . . . . . . . . . . . . . . . . . . . 25
4.4 Invariant Form of Maxwell’s Equations . . . . . . . . . . . . . . . 27
5 The Simplest Classical Field Theory 30
5.1 The Continuum Limit . . . . . . . . . . . . . . . . . . . . . . . . 35
5.2 Normal Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
5.3 Rules of Canonical Quantization . . . . . . . . . . . . . . . . . . 39
5.4 The Algebra of Boson Operators . . . . . . . . . . . . . . . . . . 41
5.5 The Classical Limit . . . . . . . . . . . . . . . . . . . . . . . . . . 44
6 Classical Field Theory 44
6.1 The Hamiltonian Formulation . . . . . . . . . . . . . . . . . . . . 46
6.2 Symmetry and Conservation Laws . . . . . . . . . . . . . . . . . 47
6.2.1 Conservation Laws . . . . . . . . . . . . . . . . . . . . . . 47
6.2.2 Noether Charges . . . . . . . . . . . . . . . . . . . . . . . 49
6.2.3 Noether’s Theorem . . . . . . . . . . . . . . . . . . . . . . 50
6.3 The Energy-Momentum Tensor . . . . . . . . . . . . . . . . . . . 51
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