22 Electromagnetic Waves in (x,y) 240

Constant Permeability 240

Complex Formalism 241

Plane Wave in a Conducting Material 242

Interpretation of Complex Amplitudes 247

Animation of a Plane Wave 247

Non-Uniform Conductivity 249

Plane Wave in Two Different Media 249

Scanning for Resonance Frequencies 252

The Magnetic Wave Field 253

Running Wave 256

23 Two-Dimensional Resonators 260

Loss-Free Rectangular Cavity 260

Resonance Model 264

Eigenvalues and Eigenstates 266

Cavity of Circular Cross-Section 268

Degenerate Eigenstates 270

Partly Dielectric Cavity 274

24 Wave-Guides 277

Wave-Guide of Circular Cross-Section 278

Expressions for Other Field Components 280

Complete FEA for the Wave-Guide 283

Rectangular Wave-Guide 287

25 Vector Potential in (x,y) 289

Vector B Confined in the (x,y) Plane 290

Time-Sinusoidal Solutions 291

Plane Wave in Two Different Media 292

PDEs for the Electric Field 295

Non-Uniform Permeability 296

Eigenvalues and Eigenstates 299

26 Eddy Fields in (x,y) 302

Inductance of a Coaxial Cable 302

Alternating Current above a Metal Plate 306

Forces Caused by Eddy Fields 308

Transient Field due to Sudden Current 310

Direct Current above a Moving Conductor 313

Permanent Magnet above a Moving Plate 316

27 Vector Potential in (r , z) 319

Time-Sinusoidal Solution 320

PDEs for the Electric Field 321

Mutual Inductance 322

Transformer 326

AC Coil above a Metal Plate 329

Forces 331

Transients Fields 332

28 Electromagnetic Radiation 336

Radiation in (r , z) Space 337

Analytic Solution in (r ) 338

Comparing the FEA and Analytic Solutions 339

Asymptotic Boundary Conditions 341

General Cylindrical Wave in (x,y) 344

Radiation from a Triangular Bar 346

Scattering against a Metal Bar 347

29 Nearly-Spherical Waves 351

Non-Reflecting Boundary Conditions 351

Radiating Coil 353

General PDEs 357

Linear Antenna 359

30 Elementary Wave Mechanics in 1D 364

The Schrödinger Wave Equations 364

Particle Transmission 365

Particle Scattering 368

Bound Particle 372

31 Harmonic Oscillators 378

Oscillator in One Dimension 378

Expectation Values 381

Harmonic Oscillator in Two Dimensions 383

Degenerate Eigenstates 385

Harmonic Oscillator in (r , z) Space 387

32 The Hydrogen Atom in (r , z) 393

Energy Eigenstates 393

Even and Odd Eigenstates 396

Higher-Energy States 399

Higher Values of the Quantum Number m 401

Analytic Solutions for Comparison 403

Radial Extension and Energy 407

Angular Momentum 408

Mean Values for Analytic Solutions 410

Mean Values for FEA Solutions 411

Hydrogen Atom in an Axial Electric Field 412

33 The Hydrogen Molecule-Ion 416

34 Fields in Three Dimensions 421

Two Point Charges of Different Signs 421

Non-Linear Set of Point Charges 424

Laplace Equation in 3D 425

Coin in a Metal Box 428

Electrical Conduction in a Cone 431

Exploiting Symmetry 434

Glass Block in a Parallel Electric Field 435

Simple Magnet Coil 438

Steady Heat Conduction 440

Temperature Transients 444

Electromagnetic Eigenstates 445

References 449

Vocabulary 450