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Astronomy

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Celestial Coordinates

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Chemistry

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Avogadro's Number

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Balancing Chemical Equations

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The Periodic Table

Classical Physics

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Archimedes Principle

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Bernoulli Principle

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Blackbody (Cavity) Radiation and Planck's Hypothesis

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Center of Mass Frame

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Comparison Between Gravitation and Electrostatics

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Coriolis Effect

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Cyclotron Resonance

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Double Slit Experiment

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Elastic and Inelastic Collisions

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Electric Fields

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Gauss's Law of Universal Gravity

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Gravity - Force and Acceleration

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Ideal and Non-Ideal Gas Laws (van der Waal)

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Kinetic Theory of Gases

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Kirchoff's Laws

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The Laws of Thermodynamics

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The Zeeman Effect

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Climate Change

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Cosmology

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Cosmic Background Radiation and Decoupling

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Geometries of the Universe

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Inflation Theory

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Periodically and Continuously Compounded Interest

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Repurchase versus Dividend Analysis

General Relativity

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Accelerated Reference Frames - Rindler Coordinates

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Catalog of Spacetimes

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Dirac Equation in Curved Spacetime

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Einstein's Field Equations

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Gravitational Time Dilation

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Gravitational Waves

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Quantum Gravity

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Relativistic, Cosmological and Gravitational Redshift

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The Area Metric

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World Lines Refresher

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Classical Field Theory

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Euler-Lagrange Equation

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Ex: Newtonian, Lagrangian and Hamiltonian Mechanics

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Hamiltonian Formulation

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Liouville's Theorem

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Lecture Notes on International Economics

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Lecture Notes on Macroeconomics

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Macroeconomic Policy

Mathematics

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Amplitude, Period and Phase

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Augmented Matrices and Cramer's Rule

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Basic Group Theory

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Basic Representation Theory

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Binomial Theorem (Pascal's Triangle)

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Building Groups From Other Groups

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Completing the Square

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Complex Numbers

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Composite Functions

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Conformal Transformations

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Conjugate Pair Theorem

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Contravariant and Covariant Components of a Vector

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Eigenvectors and Eigenvalues

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Euler Formula for Polyhedrons

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Factoring of a³ +/- b³

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Fourier Series and Transforms

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Gauss's Divergence Theorem

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Grassmann and Clifford Algebras

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Heron's Formula

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Index Notation (Tensors and Matrices)

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Integration By Parts

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Introduction to Conformal Field Theory

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Inverse of a Function

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Law of Sines and Cosines

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Line Integrals, ∮

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Matrices and Determinants

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Matrix Exponential

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Mean Value and Rolle's Theorem

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Modulus Equations

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Orthogonal Curvilinear Coordinates

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Piecewise Functions

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Polar Coordinates

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Polynomial Division

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Regular Polygons

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Sets, Groups, Modules, Rings and Vector Spaces

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Similar Matrices and Diagonalization

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Spherical Trigonometry

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Stirling's Approximation

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Sum and Differences of Squares and Cubes

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Symmetric Groups

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Tangent and Normal Line

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Taylor and Maclaurin Series

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The Essential Mathematics of Lie Groups

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The Integers Modulo n Under + and x

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The Limit Definition of the Exponential Function

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Tic-Tac-Toe Factoring

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Trapezoidal Rule

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Vector Calculus

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Volume Integrals

Microeconomics

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Marginal Revenue and Cost

Particle Physics

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Feynman Diagrams and Loops

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Field Dimensions

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Helicity and Chirality

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Klein-Gordon and Dirac Equations

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Regularization and Renormalization

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Scattering - Mandelstam Variables

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Spin 1 Eigenvectors

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The Vacuum Catastrophe

Probability and Statistics

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Box and Whisker Plots

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Categorical Data - Crosstabs

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Chebyshev's Theorem

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Chi Squared Goodness of Fit

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Conditional Probability

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Confidence Intervals

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Factor Analysis

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Hypothesis Testing

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Linear Regression

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Monte Carlo Methods

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Non Parametric Tests

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Pearson Correlation

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Permutations and Combinations

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Pooled Variance and Standard Error

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Probability Distributions

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Probability Rules

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Sample Size Determination

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Sampling Distributions

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Set Theory - Venn Diagrams

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Stacked and Unstacked Data

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Stem Plots, Histograms and Ogives

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Survey Data - Likert Item and Scale

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Programming and Computer Science

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How this site works ...

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More Programming Topics

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MVC Architecture

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Open Systems Interconnection (OSI) Standard - TCP/IP Protocol

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Public Key Encryption

Quantum Field Theory

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Creation and Annihilation Operators

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Field Operators for Bosons and Fermions

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Lagrangians in Quantum Field Theory

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Path Integral Formulation

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Relativistic Quantum Field Theory

Quantum Mechanics

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Basic Relationships

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Clebsch-Gordan Coefficients

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Electron Orbital Angular Momentum and Spin

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Entangled States

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Heisenberg Uncertainty Principle

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Ladder Operators

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Multi Electron Wavefunctions

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Pauli Exclusion Principle

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Pauli Spin Matrices

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Photoelectric Effect

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Position and Momentum States

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Probability Current

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Schrodinger Equation for Hydrogen Atom

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Schrodinger Wave Equation

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Schrodinger Wave Equation (continued)

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Spin 1/2 Eigenvectors

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The Differential Operator

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The Essential Mathematics of Quantum Mechanics

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The Observer Effect

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The Schrodinger, Heisenberg and Dirac Pictures

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The WKB Approximation

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Time Dependent Perturbation Theory

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Time Evolution and Symmetry Operations

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Time Independent Perturbation Theory

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Semiconductor Reliability

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The Weibull Distribution

Solid State Electronics

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Band Theory of Solids

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Fermi-Dirac Statistics

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Intrinsic and Extrinsic Semiconductors

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The P-N Junction

Special Relativity

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Electromagnetic 4 - Potential

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Energy and Momentum, E = mc²

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Lorentz Invariance

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Lorentz Transform

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Lorentz Transformation of the EM Field

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Newton versus Einstein

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Spinors - Part 1

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Spinors - Part 2

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The Lorentz Group

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Velocity Addition

Statistical Mechanics

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Black Body Radiation

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Entropy and the Partition Function

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The Harmonic Oscillator

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String Theory

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Bosonic Strings

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Extra Dimensions

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Introduction to String Theory

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Kaluza-Klein Compactification of Closed Strings

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Strings in Curved Spacetime

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Toroidal Compactification

Superconductivity

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Introduction to Superconductors

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Superconductivity (Lectures 1 - 10)

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Superconductivity (Lectures 11 - 20)

Supersymmetry (SUSY) and Grand Unified Theory (GUT)

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Chiral Superfields

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Generators of a Supergroup

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Grassmann Numbers

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Introduction to Supersymmetry

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The Gauge Hierarchy Problem

test

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The Standard Model

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Electroweak Unification (Glashow-Weinberg-Salam)

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Gauge Theories (Yang-Mills)

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Gravitational Force and the Planck Scale

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Introduction to the Standard Model

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Isospin, Hypercharge, Weak Isospin and Weak Hypercharge

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Quantum Flavordynamics and Quantum Chromodynamics

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Special Unitary Groups and the Standard Model - Part 1

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Special Unitary Groups and the Standard Model - Part 2

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Special Unitary Groups and the Standard Model - Part 3

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Standard Model Lagrangian

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The Higgs Mechanism

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The Nature of the Weak Interaction

Topology

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Units, Constants and Useful Formulas

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Last modified: January 26, 2018


Cyclotron Resonance
-------------------

. = magnetic field

. . . . . .     y
 m --->v        |
. . . . . .     +--- x
               /
. . . . . .   z 
              
B is in z direction

F_mag = q(v x B)

If q is +ve then, according to RHR, F is downwards (-y).  This will 
cause the charge to start moving in a circular fashion. Thus, 

F_centripetal = mv²/r

q(v x B) = qvBsinθ = mv²/r

qB = mv/r

v = qBr/m

ω = qB/m since v = rω 

If particle is also moving in the z direction then the motion of the
particle will be a helix.  There will be no influence in the z direction
since θ = sinθ = 0.

Velocity Detector
-----------------

  B ^  ^ E and F_E
    | /
    |/
    +---> v
   /
  F_B

For 0 deflection F_E = F_B

qE = qvB

Thus, v = E/B