Quantum 101

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...

Table of Contents Introduction What Are Canonical Transformations? Motivation: Why Use Canonical Transformations? The Symplectic Structure Poisson Brackets and Invariance The Fundamental Condition for Canonicity Examples of Canonical Transformations Generating Functions: The...

Table of Contents Introduction What Is Action in Physics? The Principle of Least Action Historical Development Action and the Lagrangian Deriving the Euler-Lagrange Equation Physical Meaning: Why Minimize Action? Examples of Least...

Table of Contents Introduction From Lagrangian to Hamiltonian The Hamiltonian Function Phase Space and Generalized Momentum Deriving Hamilton’s Equations Simple Example: Harmonic Oscillator Hamiltonian vs Lagrangian Mechanics Symmetries and Conservation Laws Poisson Brackets Canonical...

Table of Contents Introduction Why Go Beyond Newton? Generalized Coordinates Principle of Least Action The Lagrangian Function Euler-Lagrange Equation Simple Example: Free Particle Simple Harmonic Oscillator in Lagrangian Formalism Atwood Machine via Lagrangian Constraints...

Table of Contents Introduction What Is an Oscillator? The Simple Harmonic Oscillator (SHO) Equation of Motion for SHO Energy in Simple Harmonic Motion Phase Space Representation Damped Harmonic Oscillator Driven Harmonic Oscillator Resonance...

Table of Contents Introduction What is a Central Force? Characteristics of Central Forces Equations of Motion in Central Force Fields Conservation Laws in Central Force Problems Effective Potential and Radial...

Table of Contents Introduction What Is a Newtonian System? Newton’s Three Laws of Motion Concept of Inertial Frames Force and Mass: The Core Ingredients Types of Forces in Newtonian Mechanics Free...

Table of Contents Introduction Historical Context and Importance Kinematics: Describing Motion Newton’s Laws of Motion Work, Energy, and Power Conservation Laws Rotational Dynamics Oscillatory Motion and Harmonic Systems Central Forces and Planetary Motion Lagrangian...