Modern Physics with Numerical Methods

Timo Budarz, Ronan Downes, Mar 16, 2020

This is an open-source, modern physics textbook typically for the third semester students majoring in engineering, physics or chemistry. An emphasis is placed on fundamental principles as well as numerical solutions to equations where no analytical solutions exist. The content begins with optics and uses that as a stepping stone to wave phenomena and quantum systems.

Table of Contents

  1. Geometric Optics I
    1. Introduction
    2. Ray Tracing Basics
    3. Ray Tracing with Curved Mirrors
    4. Heiligenschein and Albedo
    5. Color
    6. PROBLEMS
    7. Lab Exercise
  2. Geometric Optics II
    1. Refraction
    2. Snell's Law
    3. Critical Angle
    4. Polarization
    5. Dispersion and Rainbows
    6. Thin Lenses
    7. Human Eye
    8. Fermat's Principle
    9. PROBLEMS
    10. Lab Exercises - Thin Lenses, Brewster's Law
    11. Lab Exercise - Crossed Polarizers
  3. Waves
    1. Waves
    2. PROBLEMS
  4. Interference
    1. Wave Interference
    2. Thin Films
    3. Young's Double Slit Experiment
    4. Multiple Slits
    5. PROBLEMS
  5. Diffraction
    1. Single Slit Diffraction
    2. Circular Apertures and Resolving Power
    3. Angular Resolution
    4. PROBLEMS
    5. Lab Exercise
  6. Music and Resonance
    1. Resonance
    2. Resonant Frequencies
    3. Resonance In Musical Instruments
    4. The Musical Scale
    5. Standing Waves and Resonance
    6. String and Pipe Modes
    7. Beats
    8. Doppler Effect
    9. The Pleasure of Music
    10. PROBLEMS
    11. Lab Exercise
    12. Lab Exercise II
  7. Quantization and Waves
    1. Background
    2. The Field
    3. Quantization
    4. Blackbody Radiation
    5. Photoelectric Effect
    6. Light Quanta
    7. Is a Photon a Particle?
    8. What are Field Quanta?
    9. PROBLEMS
  8. Quantizing Nature: A first Approach
    1. Phase, Waves and "Particles"
    2. Wave Nature of "Particles"
    3. Wilson-Sommerfeld Quantization Condition
    4. Wilson-Sommerfeld Application: 1D Electron Wave
    5. Wilson-Sommerfeld Application: Atomic Structure
    6. W-S Quantum Harmonic Oscillator
    7. PROBLEMS
  9. Quantum Mechanics
    1. Classical Wave Equation
    2. Schrödinger's Equation
    3. Properties of the Wave Function
    4. "Particle" in a 1D Box
    5. Quantum Tunneling
    6. Quantum Harmonic Oscillator
    7. PROBLEMS
    8. Wave Function Lab
  10. Special Relativity
    1. The Postulates
    2. Some Definitions
    3. Relativistic Velocity Addition
    4. Time Dilation
    5. Length Contraction
    6. Momentum and Energy
    7. Energy Momentum Relation
    8. PROBLEMS
  11. Heat Transfer
    1. Convection
    2. Conduction
    3. Thermal Radiation
    4. Evaporative Cooling
    5. The Effect of Scale
    6. PROBLEMS
  12. Fundamental Physics
    1. Breaking it Down
    2. Nuclear Structure
    3. Binding Energy
    4. Radioactive Decay
    5. Decay Schemes
    6. PROBLEMS
  13. Astrophysics and Cosmology
    1. Where are We?
    2. The Milky Way
    3. One
    4. Origins
    5. General Relativity and Expansion
    6. Numerical Solution to Friedmann Equation
  14. Answers to Problems
    1. Answers
    2. Interference

1.

Geometric Optics I

  • 1. Introduction
  • 2. Ray Tracing Basics
  • 3. Ray Tracing with Curved Mirrors
  • 4. Heiligenschein and Albedo
  • 5. Color
  • 6. PROBLEMS
  • 7. Lab Exercise

1.1.

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1.2.

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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2.

Geometric Optics II

  • 1. Refraction
  • 2. Snell's Law
  • 3. Critical Angle
  • 4. Polarization
  • 5. Dispersion and Rainbows
  • 6. Thin Lenses
  • 7. Human Eye
  • 8. Fermat's Principle
  • 9. PROBLEMS
  • 10. Lab Exercises - Thin Lenses, Brewster's Law
  • 11. Lab Exercise - Crossed Polarizers

2.1.

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2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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2.7.

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2.8.

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2.9.

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2.10.

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2.11.

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3.

Waves

This chapter is an introduction to traveling waves and all the fun things that can occur when multiple waves meet.

  • 1. Waves
  • 2. PROBLEMS

3.1.

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3.2.

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4.

Interference

  • 1. Wave Interference
  • 2. Thin Films
  • 3. Young's Double Slit Experiment
  • 4. Multiple Slits
  • 5. PROBLEMS

4.1.

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4.2.

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4.3.

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4.4.

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4.5.

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5.

Diffraction

  • 1. Single Slit Diffraction
  • 2. Circular Apertures and Resolving Power
  • 3. Angular Resolution
  • 4. PROBLEMS
  • 5. Lab Exercise

5.1.

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5.2.

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5.3.

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5.4.

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5.5.

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6.

Music and Resonance

  • 1. Resonance
  • 2. Resonant Frequencies
  • 3. Resonance In Musical Instruments
  • 4. The Musical Scale
  • 5. Standing Waves and Resonance
  • 6. String and Pipe Modes
  • 7. Beats
  • 8. Doppler Effect
  • 9. The Pleasure of Music
  • 10. PROBLEMS
  • 11. Lab Exercise
  • 12. Lab Exercise II

6.1.

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6.2.

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6.3.

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6.4.

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6.5.

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6.6.

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6.7.

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6.8.

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6.9.

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6.10.

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6.11.

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6.12.

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7.

Quantization and Waves

  • 1. Background
  • 2. The Field
  • 3. Quantization
  • 4. Blackbody Radiation
  • 5. Photoelectric Effect
  • 6. Light Quanta
  • 7. Is a Photon a Particle?
  • 8. What are Field Quanta?
  • 9. PROBLEMS

7.1.

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7.2.

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7.3.

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7.4.

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7.5.

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7.6.

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7.7.

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7.8.

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7.9.

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8.

Quantizing Nature: A first Approach

  • 1. Phase, Waves and "Particles"
  • 2. Wave Nature of "Particles"
  • 3. Wilson-Sommerfeld Quantization Condition
  • 4. Wilson-Sommerfeld Application: 1D Electron Wave
  • 5. Wilson-Sommerfeld Application: Atomic Structure
  • 6. W-S Quantum Harmonic Oscillator
  • 7. PROBLEMS

8.1.

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8.2.

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8.3.

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8.4.

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8.5.

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8.6.

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8.7.

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9.

Quantum Mechanics

  • 1. Classical Wave Equation
  • 2. Schrödinger's Equation
  • 3. Properties of the Wave Function
  • 4. "Particle" in a 1D Box
  • 5. Quantum Tunneling
  • 6. Quantum Harmonic Oscillator
  • 7. PROBLEMS
  • 8. Wave Function Lab

9.1.

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9.2.

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9.3.

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9.4.

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9.5.

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9.6.

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9.7.

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9.8.

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10.

Special Relativity

  • 1. The Postulates
  • 2. Some Definitions
  • 3. Relativistic Velocity Addition
  • 4. Time Dilation
  • 5. Length Contraction
  • 6. Momentum and Energy
  • 7. Energy Momentum Relation
  • 8. PROBLEMS

10.1.

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10.2.

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10.3.

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10.4.

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10.5.

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10.6.

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10.7.

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10.8.

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11.

Heat Transfer

  • 1. Convection
  • 2. Conduction
  • 3. Thermal Radiation
  • 4. Evaporative Cooling
  • 5. The Effect of Scale
  • 6. PROBLEMS

11.1.

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11.2.

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11.3.

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11.4.

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11.5.

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11.6.

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12.

Fundamental Physics

  • 1. Breaking it Down
  • 2. Nuclear Structure
  • 3. Binding Energy
  • 4. Radioactive Decay
  • 5. Decay Schemes
  • 6. PROBLEMS

12.1.

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12.2.

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12.3.

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12.4.

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12.5.

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12.6.

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13.

Astrophysics and Cosmology

  • 1. Where are We?
  • 2. The Milky Way
  • 3. One
  • 4. Origins
  • 5. General Relativity and Expansion
  • 6. Numerical Solution to Friedmann Equation

13.1.

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13.2.

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13.3.

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13.4.

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13.5.

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13.6.

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14.

Answers to Problems

  • 1. Answers
  • 2. Interference

14.1.

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14.2.

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