PHYS212 : Lectures

Contents

• 1. From Mechanical Oscillations to Waves
  • 1.1 Complex Numbers and Complex Exponentials
  • 1.2 Simple Harmonic Oscillations
    • 1.2.1 The Differential Equation and its Solutions
    • 1.2.2 Mass and Spring
    • 1.2.3 Physical Pendulum
  • 1.3 Two Coupled Oscillators
    • 1.3.1 Double Pendulum
    • 1.3.2 Beads on a String : Transverse Modes
  • 1.4 Many Coupled Oscillators
    • 1.4.1 Beads on a String
    • 1.4.2 Compound Pendulum or Hanging Chain
  • 1.5 The Continuous Limit : Waves on a String
    • 1.5.1 The Equation of Motion : The Wave Equation
    • 1.5.2 Solutions : Plane Waves
    • 1.5.3 Normal Modes : Standing Waves
  
  
• 2. Wave Packets
  • 2.1 Periodic and Confined Packets
    • 2.1.1 Beats
    • 2.1.2 Fourier Series
    • 2.1.3 A Square Wave
  • 2.2 Localized Packets
    • 2.2.1 An alternative Fourier Series
    • 2.2.2 Fourier Transformations
    • 2.2.3 A Square Pulse
    • 2.2.4 A Square Wave Packet
    • 2.2.5 A Gaussian Pulse
  • 2.3 Fourier Analysis in Frequency and Time
    • 2.3.1 Fourier Series, Take II
    • 2.3.2 A Square Wave
    • 2.3.3 Fourier Transformations, Take II
    • 2.3.4 A Square Pulse
  • 2.4 Bandwidth Limits
  
  
• 3. Waves in Inhomogeneous Media
  • 3.1 The Hanging Cable
    • 3.1.1 The Equation of Motion
    • 3.1.2 The Solutions : Bessel Functions of Order Zero
  • 3.2 The WKB Approximation
    • 3.2.1 The Method
    • 3.2.2 Limit of Validity
    • 3.2.3 Standing Waves on an Inhomogeneous String
  
  
• 4. Acoustic Waves
  • 4.1 The Wave Equation
    • 4.1.1 Displacement Waves
    • 4.1.2 Pressure Waves
    • 4.1.3 The Speed of Sound in an Ideal Gas
  • 4.2 Energy, Power, and Intensity
    • 4.2.1 Energy Density
    • 4.2.2 Intensity
    • 4.2.3 Decibels
  • 4.3 Reflection, Refraction, and Transmission
    • 4.3.1 Plane Waves in Three Dimensions
    • 4.3.2 Planar Boundaries
  • 4.4 The Doppler Effect
    • 4.4.1 Moving Source
    • 4.4.2 Moving Observer
    • 4.4.3 Moving Source and Observer
  • 4.5 Appendix : Adiabatic Expansion of an Ideal Gas
    • 4.5.1 Specific Heats and the Gas Constant
    • 4.5.2 Adiabatic Expansion
    • 4.5.3 About $\gamma$
  
  
• 5. Electromagnetic Waves
  • 5.1 The Wave Equation
  • 5.2 Plane Waves
  • 5.3 Polarization
  • 5.4 Energy, Power, and Intensity
    • 5.4.1 Energy Density
    • 5.4.2 Intensity and the Poynting Vector
    • 5.4.3 Radiation Pressure
  • 5.5 Reflection, Refraction, and Transmission
  • 5.6 The Doppler Effect
  
  
• 6. Diffraction
  • 6.1 Double Slit, Take I
  • 6.2 Single Slit
  • 6.3 Double Slit, Take II
  
  
• 7. Quantum Mechanical Waves
  • 7.1 Wavefunctions and Probability
  • 7.2 The Schrödinger Equation
    • 7.2.1 Separation of Variables
    • 7.2.2 Plane Waves
    • 7.2.3 Aside : Convenient Units
    • 7.2.4 Standing Waves : The Infinite Square Well
  • 7.3 Continuity and Probability Current
    • 7.3.1 Defined
    • 7.3.2 Plane Waves
    • 7.3.3 Infinite Square Wells
  • 7.4 Free Particles
    • 7.4.1 Potential Steps
    • 7.4.2 Square Barriers and Tunneling
    • 7.4.3 Potential Ramps and the WKB Approximation
    • 7.4.4 Gaussian Wave Packets
  • 7.5 Bound Particles
    • 7.5.1 A Packet in a Box
    • 7.5.2 Finite Square Well Review
    • 7.5.3 The Quantum Harmonic Oscillator
    • 7.5.4 WKB Thinking : Qualitative Sketches
  • 7.6 Time Dependent Perturbation Theory
    • 7.6.1 The Coupled Equations
    • 7.6.2 First Order Corrections
    • 7.6.3 Second Order Corrections
  • 7.7 Transitions and Radiation
    • 7.7.1 Electric Dipole (E1) Transitions
    • 7.7.2 Selection Rules
    • 7.7.3 Spontaneous Emission and Lifetimes
    • 7.7.4 E1 Transitions of an Electron Oscillator
  
  
• A. Animations

Copyright © 2003-2009, Lewis A. Riley

Updated Wed Jan 18 09:51:28 2006