Nuclear and Particle Physics

Nuclear and Particle Physics is the branch of physics that studies the structure, properties, and behavior of atomic nuclei and the fundamental particles that constitute all matter and radiation. It investigates the interactions between protons and neutrons, governed by the strong nuclear force, which explains phenomena like radioactivity, nuclear fission, and fusion. This field also delves deeper to identify the ultimate elementary particles, such as quarks and leptons, and the fundamental forces that govern their interactions, all of which are systematically cataloged within the framework of the Standard Model.

1. Foundational Concepts
   1. Historical Development
      1. Early Atomic Models
         1. Dalton's Atomic Theory
         2. Thomson's Plum Pudding Model
         3. Rutherford's Nuclear Model
      2. Discovery of Fundamental Particles
         1. Discovery of the Electron
            1. Cathode Ray Experiments
            2. Thomson's Charge-to-Mass Ratio Measurement
         2. Discovery of the Proton
            1. Goldstein's Canal Rays
            2. Rutherford's Identification
         3. Discovery of the Neutron
            1. Chadwick's Experiment
            2. Beryllium Bombardment
         4. Discovery of the Positron
            1. Anderson's Cloud Chamber Observations
            2. Cosmic Ray Studies
      3. Key Experimental Milestones
         1. Rutherford's Gold Foil Experiment
            1. Experimental Setup and Procedure
            2. Scattering Results and Analysis
            3. Nuclear Model Implications
         2. Millikan's Oil Drop Experiment
         3. Franck-Hertz Experiment
      4. Early Particle Discoveries
         1. Discovery of the Muon
         2. Discovery of the Pion
         3. Discovery of Strange Particles
   2. Essential Quantum Mechanics
      1. Wave-Particle Duality
         1. Planck's Quantum Hypothesis
         2. Photoelectric Effect
            1. Einstein's Explanation
            2. Photon Concept
         3. Compton Scattering
            1. Experimental Evidence
            2. Energy and Momentum Conservation
         4. de Broglie Hypothesis
            1. Matter Waves
            2. Wavelength Formula
         5. Davisson-Germer Experiment
      2. Quantum Mechanical Framework
         1. The Schrödinger Equation
            1. Time-Dependent Form
            2. Time-Independent Form
            3. Physical Interpretation
         2. Wavefunctions and Probability
            1. Born Interpretation
            2. Normalization Conditions
            3. Probability Current Density
         3. Superposition Principle
            1. Linear Combinations of States
            2. Interference Effects
      3. Quantum Operators and Observables
         1. Operator Formalism
            1. Position and Momentum Operators
            2. Hermitian Operators
            3. Commutation Relations
         2. Eigenvalue Problems
            1. Eigenvalues and Eigenstates
            2. Measurement Postulate
            3. Expectation Values
         3. Uncertainty Principle
            1. Heisenberg Uncertainty Relations
            2. Energy-Time Uncertainty
      4. Simple Quantum Systems
         1. Particle in a Box
            1. Infinite Square Well
            2. Energy Levels and Wavefunctions
         2. Quantum Harmonic Oscillator
            1. Energy Eigenvalues
            2. Creation and Annihilation Operators
         3. Hydrogen Atom
            1. Radial and Angular Solutions
            2. Energy Levels and Degeneracy
      5. Angular Momentum and Spin
         1. Orbital Angular Momentum
            1. Quantum Numbers
            2. Spherical Harmonics
         2. Intrinsic Spin
            1. Spin-1/2 Particles
            2. Pauli Matrices
            3. Spinors
         3. Addition of Angular Momenta
            1. Clebsch-Gordan Coefficients
            2. Total Angular Momentum
         4. Spin-Orbit Coupling
            1. Fine Structure
            2. j-j and L-S Coupling
      6. Quantum Statistics
         1. Identical Particles
            1. Symmetry and Antisymmetry
            2. Exchange Interactions
         2. Pauli Exclusion Principle
            1. Fermions and Bosons
            2. Consequences for Atomic Structure
         3. Statistical Distributions
            1. Fermi-Dirac Statistics
            2. Bose-Einstein Statistics
      7. Quantum Tunneling
         1. Barrier Penetration
            1. Transmission and Reflection Coefficients
            2. WKB Approximation
         2. Applications
            1. Alpha Decay
            2. Scanning Tunneling Microscopy
   3. Special Relativity
      1. Foundations of Special Relativity
         1. Historical Context
            1. Michelson-Morley Experiment
            2. Lorentz-FitzGerald Contraction
         2. Einstein's Postulates
            1. Principle of Relativity
            2. Constancy of Light Speed
      2. Lorentz Transformations
         1. Coordinate Transformations
            1. Space and Time Coordinates
            2. Inverse Transformations
         2. Relativistic Effects
            1. Time Dilation
            2. Length Contraction
            3. Relativity of Simultaneity
         3. Velocity Addition Formula
            1. Relativistic Velocity Composition
            2. Limiting Cases
      3. Relativistic Mechanics
         1. Four-Vector Formalism
            1. Four-Position
            2. Four-Velocity
            3. Four-Acceleration
         2. Energy-Momentum Relations
            1. Relativistic Energy
            2. Relativistic Momentum
            3. Energy-Momentum Four-Vector
         3. Mass-Energy Equivalence
            1. Rest Mass Energy
            2. Binding Energy
            3. Mass Defect
         4. Invariant Mass
            1. Definition and Properties
            2. Multi-Particle Systems
            3. Threshold Calculations
      4. Applications in Particle Physics
         1. Particle Kinematics
            1. Collision Dynamics
            2. Center-of-Mass Frame
         2. Relativistic Quantum Mechanics
            1. Klein-Gordon Equation
            2. Dirac Equation