The WKB Approximation

Search by keyword:

Astronomy

Astronomical Distance Units .

Celestial Coordinates .

Celestial Navigation .

Location of North and South Celestial Poles .

Chemistry

Avogadro's Number .

Balancing Chemical Equations

Stochiometry

The Periodic Table .

Classical Mechanics

Blackbody Radiation .

Classical Physics

Archimedes Principle

Bernoulli Principle

Center of Mass Frame

Comparison Between Gravitation and Electrostatics

Double Slit Experiment

Elastic and Inelastic Collisions .

Gauss's Law of Universal Gravity .

Gravity - Force and Acceleration

Hooke's law

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

Kinetic Theory of Gases .

Kirchoff's Laws

Maxwell's Equations .

Moments and Torque

Nuclear Spin

One Dimensional Wave Equation .

Pascal's Principle

Phase and Group Velocity

Poiseuille's Law

Refractive Index

Rotational Dynamics

Simple Harmonic Motion

Specific Heat, Latent Heat and Calorimetry

The Gas Laws

The Laws of Thermodynamics

Climate Change

Cosmology

Cosmic Background Radiation and Decoupling

CPT Symmetries

Dark Matter .

Friedmann-Robertson-Walker Equations .

Hubble's Law

Inflation Theory

Introduction to Black Holes .

Olbers' Paradox .

Planck Units .

Stephen Hawking's Last Paper

Stephen Hawking's PhD Thesis

The Big Bang Model

Vacuum Energy .

Finance and Accounting

Amortization

Annuities

Brownian Model of Financial Markets .

Capital Structure

Dividend Discount Formula

Lecture Notes on International Financial Management

NPV and IRR

Periodically and Continuously Compounded Interest

Repurchase versus Dividend Analysis

Game Theory

The Truel .

General Relativity

Basis One-forms .

Catalog of Spacetimes

Curvature and Parallel Transport

Einstein's Field Equations

Geodesics

Gravitational Waves

Hyperbolic Motion and Rindler Coordinates .

Quantum Gravity

Ricci Decomposition .

Ricci Flow .

Stress-Energy-Momentum Tensor .

Tensors

The Area Metric

The Dirac Equation in Curved Spacetime .

The Equivalence Principal

The Essential Mathematics of General Relativity

The Induced Metric

The Light Cone .

The Metric Tensor .

The Principle of Least Action in Relativity .

Vierbein (Frame) Fields

Group Theory

Basic Group Theory .

Basic Representation Theory .

Building Groups From Other Groups .

Sets, Groups, Modules, Rings and Vector Spaces

Symmetric Groups .

The Integers Modulo n Under + and x .

Lagrangian and Hamiltonian Mechanics

Classical Field Theory .

Euler-Lagrange Equation .

Ex: Newtonian, Lagrangian and Hamiltonian Mechanics .

Hamiltonian Formulation .

Liouville's Theorem

Symmetry and Conservation Laws - Noether's Theorem .

Macroeconomics

Lecture Notes on International Economics

Lecture Notes on Macroeconomics

Macroeconomic Policy

Mathematics

Amplitude, Period and Phase

Arithmetic and Geometric Sequences and Series .

Asymptotes

Augmented Matrices and Cramer's Rule

Binomial Theorem (Pascal's Triangle)

Completing the Square

Complex Numbers

Composite Functions

Conformal Transformations .

Conjugate Pair Theorem

Contravariant and Covariant Components of a Vector

Derivatives of Inverse Functions

Double Angle Formulas

Eigenvectors and Eigenvalues

Euler Formula for Polyhedrons

Factoring of a³ +/- b³

Fourier Series and Transforms .

Fractals

Gauss's Divergence Theorem

Grassmann and Clifford Algebras .

Heron's Formula

Index Notation (Tensors and Matrices) .

Inequalities

Integration By Parts

Introduction to Conformal Field Theory .

Inverse of a Function

Law of Sines and Cosines

Line Integrals, ∮

Logarithms and Logarithmic Equations

Matrices and Determinants

Matrix Exponential

Mean Value and Rolle's Theorem

Modulus Equations

Orthogonal Curvilinear Coordinates .

Parabolas, Ellipses and Hyperbolas

Similar Matrices and Diagonalization .

Spherical Trigonometry

Stirling's Approximation

Sum and Differences of Squares and Cubes

Symbolic Logic

Tangent and Normal Line

Taylor and Maclaurin Series .

The Essential Mathematics of Lie Groups

The Limit Definition of the Exponential Function

Tic-Tac-Toe Factoring

Mathjax

Microeconomics

Marginal Revenue and Cost

Nuclear Physics

Radioactive Decay

Particle Physics

Feynman Diagrams and Loops

Field Dimensions

Helicity, Chirality and Weyl Spinors .

Klein-Gordon and Dirac Equations .

Regularization and Renormalization

Scattering - Mandelstam Variables

Spin 1 Eigenvectors .

Probability and Statistics

Box and Whisker Plots

Buffon's Needle .

Categorical Data - Crosstabs

Chebyshev's Theorem

Chi Squared Goodness of Fit

Conditional Probability

Permutations and Combinations

Pooled Variance and Standard Error

Probability Distributions

Probability Rules

Sample Size Determination

Sampling Distributions

Set Theory - Venn Diagrams

Stacked and Unstacked Data

Stem Plots, Histograms and Ogives

Survey Data - Likert Item and Scale

Tukey's Test

Two-Way ANOVA

Programming and Computer Science

Hashing .

How this site works ... .

More Programming Topics

MVC Architecture .

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

Public Key Encryption .

Quantitative Methods for Business

Waiting Lines

Quantum Computing

Density Operators and Mixed States .

Entangled States .

The Qubit .

Quantum Field Theory

Creation and Annihilation Operators

Field Operators for Bosons and Fermions

Lagrangians in Quantum Field Theory

Path Integral Formulation

Relativistic Quantum Field Theory

Quantum Mechanics

Bohr Atom

Clebsch-Gordan Coefficients .

Commutators

Dyson Series

Electron Orbital Angular Momentum and Spin

Heisenberg Uncertainty Principle

Ladder Operators .

Multi Electron Wavefunctions .

Pauli Spin Matrices

Photoelectric Effect .

Position and Momentum States .

Probability Current

Schrodinger Equation for Hydrogen Atom .

Schrodinger Wave Equation

Spin 1/2 Eigenvectors

The Differential Operator

The Essential Mathematics of Quantum Mechanics

The Quantum Harmonic Oscillator .

The Schrodinger, Heisenberg and Dirac Pictures

The WKB Approximation

Time Dependent Perturbation Theory

Time Evolution and Symmetry Operations

Time Independent Perturbation Theory

Wavepackets

Semiconductor Reliability

The Weibull Distribution

Solid State Electronics

Band Theory of Solids .

Fermi-Dirac Statistics .

Intrinsic and Extrinsic Semiconductors .

The MOSFET

The P-N Junction

Special Relativity

4-vectors .

Electromagnetic (Faraday) Tensor .

Energy and Momentum in Special Relativity, E = mc² .

Invariance of the Velocity of Light .

Lorentz Invariance .

Lorentz Transform .

Lorentz Transformation of the EM Field .

Newton versus Einstein

Spinors - Part 1 .

Spinors - Part 2 .

The Continuity Equation .

The Lorentz Group .

Statistical Mechanics

Entropy and the Partition Function

The Harmonic Oscillator

The Ideal Gas

String Theory

Bosonic Strings

Extra Dimensions

Introduction to String Theory

Kaluza-Klein Compactification of Closed Strings

Strings in Curved Spacetime

Toroidal Compactification

Superconductivity

Bardeen–Cooper–Schrieffer Theory

BCS Theory

Cooper Pairs

Introduction to Superconductivity .

Superconductivity (Lectures 1 - 10)

Superconductivity (Lectures 11 - 20)

Supersymmetry (SUSY) and Grand Unified Theory (GUT)

Chiral Superfields

Generators of a Supergroup

Grassmann Numbers

Introduction to Supersymmetry

The Gauge Hierarchy Problem

The Standard Model

Electroweak Unification (Glashow-Weinberg-Salam)

Gauge Theories (Yang-Mills)

Gravitational Force and the Planck Scale

Introduction to the Standard Model

Isospin, Hypercharge, Weak Isospin and Weak Hypercharge

Quantum Flavordynamics and Quantum Chromodynamics

Special Unitary Groups and the Standard Model

Standard Model Lagrangian

The Higgs Mechanism

The Nature of the Weak Interaction

Topology

Units, Constants and Useful Formulas

Constants

Redshift Academy