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Contents
Contents
Oscillations and Waves
Richard Fitzpatrick
Professor of Physics
The University of Texas at Austin
Contents
Simple Harmonic Oscillation
Introduction
Mass on Spring
Simple Harmonic Oscillator Equation
LC Circuit
Simple Pendulum
Compound Pendulum
Exercises
Damped and Driven Harmonic Oscillation
Introduction
Damped Harmonic Oscillation
Quality Factor
LCR Circuit
Driven Damped Harmonic Oscillation
Driven LCR Circuit
Transient Oscillator Response
Exercises
Coupled Oscillations
Introduction
Two Spring-Coupled Masses
Two Coupled LC Circuits
Three Spring-Coupled Masses
Exercises
Transverse Standing Waves
Introduction
Normal Modes of Beaded String
Normal Modes of Uniform String
General Time Evolution of Uniform String
Exercises
Longitudinal Standing Waves
Introduction
Spring-Coupled Masses
Longitudinal Waves on Thin Elastic Rod
Sound Waves in Ideal Gas
Fourier Analysis
Exercises
Traveling Waves
Introduction
Standing Waves in Finite Continuous Medium
Traveling Waves in Infinite Continuous Medium
Wave Interference
Energy Conservation
Transmission Lines
Normal Reflection and Transmission at Interfaces
Electromagnetic Waves
Doppler Effect
Wave Propagation in Inhomogeneous Media
Exercises
Multi-Dimensional Waves
Introduction
Plane Waves
Three-Dimensional Wave Equation
Cylindrical Waves
Spherical Waves
Oscillation of an Elastic Sheet
Polarization of Electromagnetic Waves
Laws of Geometric Optics
Fresnel Relations
Total Internal Reflection
Birefringence
Sound Waves in Fluids
Exercises
Wave Pulses
Introduction
Fourier Transforms
Dirac Delta Function
General Solution of 1D Wave Equation
Bandwidth
Bandwidth Theorem
Exercises
Dispersive Waves
Introduction
Pulse Propagation
Electromagnetic Waves in Unmagnetized Plasmas
Faraday Rotation
Electromagnetic Waves in Magnetized Plasmas
Low-Frequency EM Waves in Magnetized Plasmas
Parallel EM Waves in Magnetized Plasmas
Perpendicular EM Waves in Magnetized Plasmas
Electromagnetic Waves in Conductors
Waveguides
Pulse Propagation in Two Dimensions
Gravity Waves
Wave Drag on Ships
Ship Wakes
Capillary Waves
Exercises
Wave Optics
Introduction
Two-Slit Interference
Coherence
Multi-Slit Interference
Thin-Film Interference
One-Dimensional Fourier Optics
Single-Slit Diffraction
Multi-Slit Diffraction
Two-Dimensional Fourier Optics
Huygens–Fresnel Principle
Babinet's Principle
Diffraction from Rectangular Aperture
Diffraction from Straight Edge
Diffraction from Rectangular Slit
Diffraction from Straight Wire
Diffraction from Circular Aperture
Diffraction from Circular Disk
Exercises
Wave Mechanics
Introduction
Photoelectric Effect
Electron Diffraction
Representation of Waves via Complex Numbers
Schrödinger's Equation
Probability Interpretation of Wavefunction
Wave Packets
Heisenberg's Uncertainty Principle
Wavefunction Collapse
Stationary States
Particle in Finite Square Potential Well
Square Potential Barrier
WKB Approximation
Cold Emission
Alpha Decay
Three-Dimensional Wave Mechanics
Particle in Box
Degenerate Electron Gas
White-Dwarf Star
Exercises
Physical Constants
Useful Mathematics
Calculus
Series Expansions
Trigonometric Identities
Electromagnetic Theory
Bibliography
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