Wave Theory Reference

Advanced Electrodynamics

Maxwell Laws

Gauge Theory

Wave Solution

Polarization

Maxwell Equations (Differential)

\[ \nabla \cdot \mathbf{E} = \rho / \epsilon_0 \]
\[ \nabla \cdot \mathbf{B} = 0 \]
\[ \nabla \times \mathbf{E} = -\partial \mathbf{B} / \partial t \]
\[ \nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \mu_0 \epsilon_0 \partial \mathbf{E} / \partial t \]

Conservation Laws

Poynting's Theorem:

\[ \frac{\partial u}{\partial t} + \nabla \cdot \mathbf{S} = -\mathbf{J} \cdot \mathbf{E} \]

Density \(u\):

\[ \frac{1}{2}(\epsilon_0 E^2 + \frac{1}{\mu_0} B^2) \]

Flux \(\mathbf{S}\):

\[ \frac{1}{\mu_0}(\mathbf{E} \times \mathbf{B}) \]

Gauges

Coulomb Gauge:

\[ \nabla \cdot \mathbf{A} = 0 \ foliage]

Lorenz Gauge:

\[ \nabla \cdot \mathbf{A} + \frac{1}{c^2} \frac{\partial \Phi}{\partial t} = 0 \]

Retarded Potentials

\[ \Phi(\mathbf{r}, t) = \frac{1}{4\pi\epsilon_0} \int \frac{\rho(\mathbf{r}', t_r)}{|\mathbf{r} - \mathbf{r}'|} d\mathbf{r}' \]

\[ \mathbf{A}(\mathbf{r}, t) = \frac{\mu_0}{4\pi} \int \frac{\mathbf{J}(\mathbf{r}', t_r)}{|\mathbf{r} - \mathbf{r}'|} d\mathbf{r}' \]

Where retarded time \(t_r = t - |\mathbf{r} - \mathbf{r}'|/c\)

Monochromatic Waves

\[ \mathbf{E} = \mathbf{E}_0 e^{i(\mathbf{k} \cdot \mathbf{r} - \omega t)} \]

Wave Number: \(k = \omega/v = n\omega/c\)

Transverse: \(\mathbf{k} \cdot \mathbf{E}_0 = 0\)

Magnetic: \(\mathbf{B}_0 = \frac{1}{\omega} (\mathbf{k} \times \mathbf{E}_0)\)

Intensity: \(I = \frac{1}{2} c \epsilon_0 n E_0^2\)

Polarization Calculus

Jones Vector

Lin Horz: \(\begin{pmatrix} 1 \\ 0 \end{pmatrix}\)

Lin Vert: \(\begin{pmatrix} 0 \\ 1 \end{pmatrix}\)

RHC: \(\frac{1}{\sqrt{2}} \begin{pmatrix} 1 \\ -i \end{pmatrix}\)

Stokes (I,Q,U,V)

\(I = |E_x|^2 + |E_y|^2\)

\(Q = |E_x|^2 - |E_y|^2\)

\(U = 2\text{Re}(E_x E_y^*)\)

\(V = 2\text{Im}(E_x E_y^*)\)

Degree of Polarization: \(P = \frac{\sqrt{Q^2 + U^2 + V^2}}{I}\)

Advanced Electrodynamics Potentials and Wave Theory

Field Conservation Laws

Gauge Invariance Mastery

Causal Wave Solutions

Plane Wave Dynamics

Polarization Matrix Algebra

Conservation Field Analysis Worksheet

Conservation Field Slides

Wave Theory Cheat Sheet

Potentials and Gauge Slides

Gauge Transformation Worksheet

Green's Function Slides

Retarded Potentials Worksheet

Plane Wave Dynamics Slides

Plane Wave Analysis Worksheet

Polarization Matrix Slides

Polarization Matrix Worksheet

Similar Sequences

Le Pouvoir Solaire

dimitri0681

Metabolic Engines

dimitri0681

Human Nature and Conflict

Entropy and Energy Flow

Root Cause Investigation

Strategic Hazard Assessment and Risk Control

OSHA Standards and Compliance

Agitation Anatomy

Access Keys: Screen Reader Navigation and Context

Mouseless Mastery Sequence

Ethical Design Standards and Intellectual Property

Responsive Layouts and Mobile-First Development

Code Canvas

CSS Layout Mastery

Professional Web Portfolio Design

Web Launch Blueprint

User Centered Design Sequence

Semantic Scribe

Syntax Studio Fundamentals

Portfolio Pro Sequence

Inclusive Design Standards

Layout Logic

Professional Deployment and Site Maintenance

Inclusive Web Standards

User Experience Research and Interface Design

Architecting the Web

Semantic HTML and Information Architecture

Expression Mechanics

Experimental Functional Analysis Procedures

Scenic Automation and Structural Engineering

Sustainable Scenography and Material Science

Sonic Architecture

ABC Data Mastery

Behavioral Chain Reaction

Behavioral Patterns Analysis

Technical Direction and Structural Engineering

Behavioral Kinetics and Persistence

Reinforcement Foundations and Mechanisms

Reinforcement Masters

Reinforcement Schedules and Token Economies