Quantum 101

Table of Contents Introduction The Limitations of Special Relativity Equivalence Principle From Newtonian Gravity to Geometry Spacetime Curvature Tensors and the Metric Tensor Einstein’s Field Equations Geodesics and Motion in Curved Spacetime Gravitational...

Table of Contents Introduction Classical vs Relativistic Dynamics The Need for Redefining Momentum Four-Momentum and the Relativistic Framework Relativistic Momentum Relativistic Energy Energy-Momentum Relation Mass-Energy Equivalence Invariant Mass and Rest Energy Four-Velocity and Four-Momentum Conservation...

Table of Contents Introduction The Need for a New Transformation Einstein’s Postulates Revisited Galilean vs Lorentz Transformations Derivation of the Lorentz Transformations Time Dilation from Lorentz Transformations Length Contraction from Lorentz...

Table of Contents Introduction Historical Background and Motivation Einstein’s Postulates Galilean vs Lorentz Transformations Time Dilation Length Contraction Relativity of Simultaneity Lorentz Transformation Derivation Velocity Addition in Special Relativity Mass-Energy Equivalence Four-Vectors and Minkowski Spacetime Causality...

Table of Contents Introduction What Are Vibrations? The Simple Harmonic Oscillator Damped Oscillations Driven Oscillations and Resonance Coupled Oscillators What Are Waves? Mechanical Waves: Transverse and Longitudinal The Wave Equation Wave Parameters: Wavelength, Frequency,...

Table of Contents Introduction What Are Electromagnetic Waves? Derivation from Maxwell’s Equations Wave Equation in Free Space Characteristics of EM Waves Polarization and Vector Nature The Poynting Vector and Radiation Intensity EM...

Table of Contents Introduction Maxwell’s Equations: The Core Set What Is Free Space? Maxwell’s Equations in Free Space Derivation of Wave Equations Plane Wave Solutions Properties of Electromagnetic Waves The Speed of...

Table of Contents Introduction Electric Charge and Coulomb’s Law Electric Fields and Gauss’s Law Electric Potential and Energy Conductors and Dielectrics Magnetic Fields and Biot–Savart Law Ampère’s Law and Magnetic Materials Faraday’s...

Table of Contents Introduction What Is Thermodynamics? The Four Laws of Thermodynamics Internal Energy and the First Law Work, Heat, and State Functions The Concept of Entropy Entropy and Reversible vs...

Table of Contents Introduction What Is Classical Statistical Mechanics? The Need for a Statistical Approach Microstates, Macrostates, and Phase Space Liouville’s Theorem and Probability Conservation Ensembles: Microcanonical, Canonical, and Grand...

Table of Contents Introduction What Is Phase Space? Coordinates in Phase Space Trajectories and Hamiltonian Flow Volume Elements and Liouville’s Theorem What Is Symplectic Geometry? The Symplectic Form Canonical Transformations and Symplectic...

Table of Contents Introduction What Are Poisson Brackets? Mathematical Definition Physical Meaning Properties of Poisson Brackets The Role in Hamilton’s Equations Poisson Brackets and Constants of Motion Symmetries and Noether's Theorem Common Poisson...