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WAVES AND PARTICLES: INTRODUCTION TO THE FUNDAMENTAL CONCEPTS OF QUANTUM MECHANICS Electromagnetic Waves and Photons Material Particles and Matter Waves Quantum Description of a Particle; Wave Packets Particle in a Time-Independent Scalar Potential Complements THE MATHEMATICAL TOOLS OF QUANTUM MECHANICS One-Particle Wave Function Space State Space. Dirac Notation Representations in the State Space Eigenvalue Equations. Observables Two Important Examples of Representations and Observables Tensor Product of State Spaces Complements THE POSTULATES OF QUANTUM MECHANICS Introduction Statement of the Postulates The Physical Interpretation of the Postulates The Physical Implications of the Schrödinger Equation The Superposition Principle and Physical Predictions Complements APPLICATION OF THE POSTULATES TO SIMPLE CASES: TWO LEVEL SYSTEMS AND SPIN 1/2 SYSTEMS Spin 1/2 Particle: Quantization of the Angular Momentum Illustration of the Postulates in the Case of a Spin 1/2 General Study of Two-Level Systems Complements THE ONE DIMENSIONAL HARMONIC OSCILLATOR Introduction Eigenvalues of the Hamiltonian Eigenstates of the Hamiltonian Complements GENERAL PROPERTIES OF ANGULAR MOMENTUM IN QUANTUM MECHANICS Introduction: The Importance of Angular Momentum Commutation Relations Characteristic of Angular Momentum General Theory of Angular Momentum Application to Orbital Angular Momentum Complements PARTICLES IN A CENTRAL POTENTIAL. THE HYDROGEN ATOM Stationary States of a Particle in a Central Potential Motion of the Center of Mass and Relative Motion for a System of Two Interacting Particles The Hydrogen Atom Complements