MIT 8.03: Vibrations, Waves & Optics
Professor Yen-Jie Lee - 22 comprehensive lectures from mechanical oscillators to quantum waves
About This Course
MIT's 8.03 is a foundational course that develops the mathematical formalism and physical intuition for understanding wave phenomena across all of physics. Professor Yen-Jie Lee's lectures progress logically from simple harmonic motion through electromagnetic waves to modern applications in quantum mechanics and gravitational wave detection.
The course emphasizes mathematical techniques (Fourier analysis, complex notation, dispersion relations) and physical concepts(resonance, normal modes, interference, diffraction) that are essential for advanced physics courses.
Why this course is critical: The wave concepts developed here appear in plasma physics (electromagnetic waves in plasmas), quantum mechanics (wave functions), quantum field theory (field quantization), and astrophysics (gravitational waves). The mathematical tools (especially Fourier analysis) are used throughout theoretical physics.
Part I: Mechanical Vibrations and Waves (10 Lectures)
Building from simple harmonic oscillators to the wave equation. Develops fundamental concepts of resonance, normal modes, and Fourier analysis that apply throughout physics.
Periodic Oscillations, Harmonic Oscillators
Introduction to simple harmonic motion. Differential equation mx'' + kx = 0. Solutions using complex notation: x(t) = Ae^(iωt). Energy in oscillators. The harmonic oscillator as the fundamental building block of wave physics.
Video Lecture
Lecture 1: Periodic Oscillations
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Damped Free Oscillators
Adding damping: mx'' + bx' + kx = 0. Underdamped, critically damped, and overdamped cases. Q-factor and energy dissipation. Exponential decay of oscillations. Physical examples: pendulums, mechanical systems, LC circuits.
Video Lecture
Lecture 2: Damped Oscillators
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Driven Oscillators, Transient Phenomena, Resonance
Forced oscillations: mx'' + bx' + kx = F₀cos(ωt). Steady-state and transient solutions. Resonance phenomenon: amplitude peaks when driving frequency matches natural frequency. Phase relationships. Applications to mechanical and electrical systems.
Video Lecture
Lecture 3: Driven Oscillators and Resonance
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Coupled Oscillators, Normal Modes
Two coupled oscillators: matrix formulation. Eigenvalue problem for normal modes. Each normal mode oscillates at a characteristic frequency. Superposition of normal modes gives general solution. Foundation for understanding vibrations in complex systems.
Video Lecture
Lecture 4: Coupled Oscillators
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Beat Phenomena
Beats from superposition of two close frequencies: x(t) = cos(ω₁t) + cos(ω₂t). Beat frequency ω_beat = |ω₁ - ω₂|. Physical interpretation: energy transfer between oscillators. Applications: music, radio, quantum mechanics (beat phenomenon in wave packets).
Video Lecture
Lecture 5: Beat Phenomena
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Driven Oscillators, Resonance (continued)
Deeper exploration of resonance phenomena. Power absorption at resonance. Lorentzian line shape. Width of resonance peak related to damping (Q-factor). Applications: atomic spectroscopy, particle physics resonances, plasma wave absorption.
Video Lecture
Lecture 6: Resonance Phenomena
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Symmetry, Infinite Number of Coupled Oscillators
Role of symmetry in coupled oscillator systems. Degeneracy of normal mode frequencies from symmetry. Extending to infinite number of coupled oscillators: continuum limit. Transition from discrete oscillators to continuous wave equation.
Video Lecture
Lecture 7: Symmetry and Infinite Oscillators
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Translation Symmetry
Translation symmetry in infinite coupled oscillator chains. Leads to wave solutions: u(x,t) = Ae^(i(kx-ωt)). Dispersion relation ω(k) emerges from translation symmetry. Brillouin zones for periodic systems. Connection to solid state physics (phonons) and plasma physics.
Video Lecture
Lecture 8: Translation Symmetry
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Wave Equation, Standing Waves, Fourier Series
Derivation of wave equation: ∂²u/∂t² = v²∂²u/∂x². Standing waves from boundary conditions. Fourier series: any periodic function as sum of sinusoids. Normal modes of vibrating string. Applications: musical instruments, electromagnetic cavities, quantum mechanics (particle in a box).
Video Lecture
Lecture 9: Wave Equation and Fourier Series
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Traveling Waves
Traveling wave solutions: u(x,t) = f(x - vt). Wave speed v determined by medium properties. Reflection and transmission at boundaries. Impedance matching. Energy transport by waves. D'Alembert's solution of wave equation. Applications to electromagnetic waves and plasma waves.
Video Lecture
Lecture 10: Traveling Waves
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Part II: Electromagnetic Waves (5 Lectures)
Maxwell's equations and electromagnetic wave propagation. Introduces dispersion, Fourier transforms, and the uncertainty principle - essential for quantum mechanics and plasma physics.
Note: Lecture 11 is not included in the provided series. The lectures jump from Lecture 10 (Traveling Waves) to Lecture 12 (Maxwell's Equations).
Maxwell's Equations, Electromagnetic Waves
Maxwell's four equations in vacuum and media. Derivation of electromagnetic wave equation from Maxwell's equations. Speed of light c = 1/√(μ₀ε₀). Electromagnetic waves as coupled E and B fields oscillating perpendicular to propagation direction. Poynting vector and energy flux.
Video Lecture
Lecture 12: Maxwell's Equations
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Dispersive Medium, Phase Velocity, Group Velocity
Dispersion relations ω(k) in different media. Phase velocity v_p = ω/k vs group velocity v_g = dω/dk. Group velocity is the velocity of wave packets (energy transport). Dispersion causes wave packet spreading. Critical for understanding plasma waves and quantum wave packets.
Video Lecture
Lecture 13: Dispersion and Group Velocity
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Fourier Transform, AM Radio
Fourier transform for non-periodic functions: f(x) = ∫f̃(k)e^(ikx)dk. Relationship to Fourier series. Convolution theorem. Application to AM radio: amplitude modulation as wave packet. Bandwidth and information transmission. Essential mathematical tool for quantum mechanics.
Video Lecture
Lecture 14: Fourier Transform
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Uncertainty Principle, 2D Waves
Uncertainty principle from Fourier analysis: Δx·Δk ≥ 1/2. Cannot simultaneously localize a wave packet in both position and wave number. Direct connection to Heisenberg uncertainty Δx·Δp ≥ ℏ/2. Extension to 2D waves: circular waves, plane waves in 2D.
Video Lecture
Lecture 15: Uncertainty Principle
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2D and 3D Waves, Snell's Law
Wave equation in 2D and 3D. Plane waves: E = E₀e^(i(k·r - ωt)). Boundary conditions at interfaces between different media. Derivation of Snell's law from continuity of wave fronts. Reflection and refraction. Total internal reflection. Applications to optics and plasma boundaries.
Video Lecture
Lecture 16: 2D/3D Waves and Snell's Law
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Part III: Optics (7 Lectures)
Polarization, interference, and diffraction demonstrate wave nature of light. Concludes with quantum waves and gravitational waves - modern applications of wave physics.
Polarization, Polarizer
Polarization states of electromagnetic waves: linear, circular, elliptical. Jones vectors and matrices. Polarizers: Malus's law I = I₀cos²θ. Applications: sunglasses, LCD screens, plasma diagnostics (polarimetry), stress analysis.
Video Lecture
Lecture 17: Polarization
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Wave Plates, Radiation
Quarter-wave and half-wave plates for manipulating polarization. Conversion between linear and circular polarization. Electromagnetic radiation from accelerating charges: dipole radiation pattern. Power radiated ∝ a². Applications: antennas, synchrotron radiation, bremsstrahlung in plasmas.
Video Lecture
Lecture 18: Wave Plates and Radiation
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Waves in Medium
Electromagnetic waves in dielectric media. Index of refraction n = √(εᵣμᵣ). Dispersion: n(ω). Absorption and complex refractive index. Kramers-Kronig relations connecting absorption and dispersion. Plasma frequency and cutoff for electromagnetic wave propagation in plasmas.
Video Lecture
Lecture 19: Waves in Medium
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Interference, Soap Bubble
Wave interference: constructive and destructive. Coherence requirement for interference. Thin film interference: soap bubbles, oil films, anti-reflection coatings. Path difference and phase shifts. Applications: interferometry for plasma diagnostics, precision measurements, LIGO.
Video Lecture
Lecture 20: Interference
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Phased Radar, Single Electron Interference
Phased array radar: controlling beam direction electronically. Interference from multiple sources. Single electron double-slit experiment: wave-particle duality. Each electron interferes with itself! Demonstrates quantum nature of matter. Connection to quantum mechanics and measurement problem.
Video Lecture
Lecture 21: Phased Radar and Quantum Interference
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Diffraction, Resolution
Diffraction from single and multiple slits. Fraunhofer diffraction. Diffraction limit on resolution: Rayleigh criterion θ_min ≈ λ/D. Applications: telescope resolution, microscopy limits, X-ray crystallography. Fourier optics: diffraction as Fourier transform of aperture function.
Video Lecture
Lecture 22: Diffraction and Resolution
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Quantum Waves and Gravitational Waves
Course conclusion connecting classical waves to modern physics. Quantum wave functions as probability amplitude waves. Schrödinger equation as wave equation. Gravitational waves from Einstein's general relativity: ripples in spacetime. LIGO detection in 2015. Wave phenomena from smallest to largest scales.
Video Lecture
Lecture 23: Quantum and Gravitational Waves
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Study Guide
Recommended Study Approach:
- • Part I (Lectures 1-10): Master the mathematics of oscillators and waves. Work through derivations of normal modes and the wave equation.
- • Part II (Lectures 12-16): Focus on Fourier transform techniques and dispersion relations. These are essential for QM and plasma physics.
- • Part III (Lectures 17-23): Understand interference and diffraction deeply - they demonstrate wave-particle duality in quantum mechanics.
Key Mathematical Skills to Develop:
- • Complex exponentials: e^(iωt) notation for oscillations and waves
- • Eigenvalue problems: finding normal modes of coupled systems
- • Fourier series and Fourier transforms: decomposing arbitrary functions
- • Dispersion relations: ω(k) and phase/group velocity calculations
- • Boundary conditions: reflection, transmission, standing waves
Connections to Other Courses:
- • Plasma Physics: Lectures 12-16 on EM waves are directly applicable to plasma wave theory
- • Quantum Mechanics: Lectures 14-15 on Fourier transforms and uncertainty principle are essential
- • QFT: Lectures 4, 7-9 on normal modes provide foundation for field quantization
- • Diagnostics: Lectures 17-23 on optics essential for experimental plasma physics
Most Important Concept: The universality of wave phenomena. The same mathematical formalism (wave equation, Fourier analysis, dispersion relations) applies to mechanical waves, electromagnetic waves, quantum wave functions, and even gravitational waves. Master these concepts once and apply them everywhere in physics.
Recommended Textbooks
Perfect companion to this course. Part of MIT Introductory Physics Series. Clear explanations, excellent problems.
For Part II (EM waves). Chapter 9 essential. Best undergraduate text for electromagnetism.
For Part III. Comprehensive optics text with beautiful illustrations and applications.