This is a "how to guide" for making beginning calculations in modern physics. The academic level is second year college physical science and engineering students. The calculations are performed in Mathematica, and stress graphical visualization, units, and numerical answers. The techniques show the student how to learn the physics without being hung up on the math. There is a continuing movement to introduce more advanced computational methods into lower-level physics courses. Mathematica is a unique tool in that code is written as "human readable" much like one writes a traditional equation on the board.
Key Features:
• Concise summary of the physics concepts.
• Over 300 worked examples in Mathematica.
• Tutorial to allow a beginner to produce fast results.
The companion code for this book can be found here: https://physics.bu.edu/~rohlf/code.html
Author(s): James W. Rohlf
Edition: 1
Publisher: CRC Press
Year: 2023
Language: English
Commentary: Publisher's PDF
Pages: 218
City: Boca Raton, FL
Tags: Wolfram Mathematica; Physics; Wolfram Language
Cover
Half Title
Title Page
Copyright Page
Contents
Preface
CHAPTER 1: Basis of Modern Physics
1.1. CHARGE AND THE ELECTRONVOLT
1.1.1. Elementary Charge
1.1.2. Strength of Electromagnetism
1.2. PLANCK’S CONSTANT
1.2.1. The Combination hc
1.2.2. Reduced Planck’s Constant (ℏ)
1.2.3. Fine Structure Constant
1.2.4. Strength of Gravity
1.3. ENERGY
1.3.1. Mass and Momentum Units
1.3.2. Kinetic and Mass Energy
1.3.3. Momentum
1.3.4. Potential Energy
1.3.5. Nuclear Binding Energy
1.3.6. Q Value
1.4. THE PHOTON
1.4.1. Wavelength and Energy
1.4.2. Speed and Frequency
1.5. DE BROGLIE WAVELENGTH
1.5.1. Particle Wave Duality
1.5.2. Wavelength and Kinetic Energy
1.5.3. Classical Regime
1.6. UNCERTAINTY PRINCIPLE
1.6.1. Position and Momentum
1.6.2. Energy and Time
CHAPTER 2: Thermal Radiation
2.1. RAYLEIGH-JEANS FORMULA
2.1.1. Average Oscillator Energy
2.1.2. Number of Modes
2.1.3. Power per Area
2.2. PLANCK FORMULA
2.2.1. Comparison with Rayleigh-Jeans
2.2.2. Planck Formula vs. Temperature
2.2.3. Radiation Peak
2.2.4. Planck Formula vs. Frequency
2.2.5. Number of Photons
2.3. STEFAN-BOLTZMANN LAW
2.4. WEIN’S LAW
CHAPTER 3: Key Processes
3.1. RADIOACTIVE DECAY
3.1.1. Decay Types
3.1.2. Decay Probability
3.1.3. Carbon Dating
3.2. MOTION OF A CHARGED PARTICLE IN ELECTRIC AND MAGNETIC FIELDS
3.2.1. Charged Particle in an Electric Field
3.2.2. Charged Particle in a Magnetic Field
3.2.3. Electron Charge-to-Mass Ratio
3.2.4. Electron Charge Measurement
3.3. PHOTOELECTRIC EFFECT
3.4. ELECTRON DIFFRACTION
3.4.1. Scattering Off a Crystal
3.4.2. Neutrons in Thermal Equilibrium
3.4.3. Quarks Inside a Proton
3.5. COMPTON SCATTERING
3.5.1. Compton Formula in Terms of Energy
3.5.2. Limiting Cases
3.5.3. Compton Formula in Terms of Wavelength
3.5.4. Relationship of λc to Other Quantities
3.6. RUTHERFORD SCATTERING
3.6.1. Effect of the Electrons
3.6.2. Scattering from a Nucleus
3.6.3. Cross Section
3.6.4. Scattering from a Thin Foil
3.7. THE WEAK INTERACTION
3.7.1. Weak Coupling
3.7.2. Neutrino Cross Section
3.7.3. Neutrino Scattering Rate
3.7.4. Neutrino Mean Free Path
CHAPTER 4: Special Relativity
4.1. BETA AND GAMMA
4.2. SPACE AND TIME
4.2.1. Time Dilation
4.2.2. Lorentz Contraction
4.3. ENERGY AND MOMENTUM
4.4. 4-VECTORS
4.4.1. Invariant Mass
4.4.2. Center of Mass
4.5. LORENTZ TRANSFORMATION
4.5.1. Transformation of Time-Space
4.5.2. Transformation of Energy-Momentum
4.6. DOPPLER EFFECT
4.6.1. Colinear Light Source
4.6.2. Redshift
4.6.3. Observation at an Angle
CHAPTER 5: Bohr Model
5.1. QUANTIZATION OF ANGULAR MOMENTUM
5.2. GROUND STATE
5.2.1. Bohr radius
5.2.2. Energy
5.3. EXCITED STATES
5.3.1. Orbits
5.3.2. Speeds
5.3.3. Energies
5.4. TRANSITIONS BETWEEN ENERGY LEVELS
5.4.1. Lyman Series
5.4.2. Balmer Series
5.4.3. Paschen Series
5.5. RYDBERG CONSTANT
5.6. REDUCED MASS
5.7. COLLAPSE OF THE BOHR ATOM
5.8. CORRESPONDENCE PRINCIPLE
5.8.1. Orbit and Radiation Frequency
5.8.2. Earth’s Orbit
5.8.3. LHC Proton
CHAPTER 6: Particle in a Box
6.1. THE POTENTIAL
6.2. THE SCHRÖDINGER EQUATION
6.3. SOLUTION
6.3.1. Wave Functions
6.3.2. Electron in a Box
6.3.3. Proton in a Box
6.4. COMPARISON WITH THE DE BROGLIE WAVELENGTH AND THE UNCERTAINTY PRINCIPLE
6.5. EXPECTATION VALUES
6.5.1. Position
6.5.2. Momentum
6.6. CONSISTENCY WITH THE UNCERTAINTY PRINCIPLE
6.7. CORRESPONDENCE PRINCIPLE
6.7.1. Phone in Box
6.7.2. Classical Probability
6.8. THREE DIMENSIONS
6.9. FINITE POTENTIAL
6.9.1. Solution Technique
6.9.2. Energy Condition
6.9.3. Solving for the Energy
6.9.4. Wave Functions
CHAPTER 7: Quantum Harmonic Oscillator
7.1. GROUND STATE
7.1.1. Wave Function
7.1.2. Energy
7.1.3. Normalization
7.1.4. Quantum Tunneling
7.1.5. Uncertainty Principle
7.2. FIRST EXCITED STATE
7.2.1. Wave Function
7.2.2. Energy
7.2.3. Normalization
7.2.4. Quantum Tunneling
7.2.5. Uncertainty Principle
7.3. GENERAL SOLUTION
7.3.1. Hermite Polynomials
7.3.2. Normalization
7.3.3. Energy
7.3.4. Wave Functions
7.4. CORRESPONDENCE PRINCIPLE
7.4.1. Large Quantum Numbers
7.4.2. Classical Probability
CHAPTER 8: Hydrogen Atom
8.1. GROUND STATE
8.1.1. Solution
8.1.2. Normalized Wave Functions
8.1.3. Radial Probability
8.1.4. Consistency with the Uncertainty Principle
8.2. FIRST EXCITED STATES
8.2.1. Wavefunctions
8.2.2. Energies
8.2.3. Radial Probability Distributions
8.3. MORE EXCITED STATES
8.4. CORRESPONDENCE PRINCIPLE
8.5. TRANSITIONS BETWEEN LEVELS
8.6. ELECTRON INTRINSIC ANGULAR MOMENTUM
8.6.1. Addition of Angular Momentum
8.6.2. Magnetic Moment
8.6.3. Zeeman Effect
8.6.4. Spin-Orbit Interaction
8.6.5. Hyperfine Splitting
8.6.6. Lamb Shift
8.6.7. The Electron g-Factor
CHAPTER 9: Statistical Physics
9.1. PROBABILITY DISTRIBUTIONS
9.1.1. Binomial Distribution
9.1.2. Poisson Distribution
9.1.3. Gaussian Distribution
9.2. MAXWELL-BOLTZMANN DISTRIBUTION
9.2.1. The Ideal Gas
9.2.2. Gas Pressure
9.2.3. Mean Free Path
9.2.4. Velocity Distribution
9.2.5. Speed Distribution
9.2.6. Energy Distribution
9.3. QUANTUM DISTRIBUTIONS
9.3.1. Bose-Einstein Distribution
9.3.2. Fermi-Dirac Distribution
9.3.3. Comparison of the Distribution Functions
9.3.4. Density of States
9.3.5. Photon Gas
9.3.6. Electron Gas
9.3.7. Superfluid Helium
CHAPTER 10: Astrophysics
10.1. THE SUN
10.1.1. Proton Cycle
10.1.2. Distance to the Sun
10.1.3. Solar Constant
10.1.4. Temperature of Sun
10.1.5. Neutrino Flux from the Sun
10.2. MAGNITUDE SCALE FOR SKY OBJECTS
10.2.1. Apparent Magnitude
10.2.2. Absolute Magnitude
10.3. THE MILKY WAY
10.4. WHITE DWARF
10.5. NEUTRON STAR
10.5.1. Density
10.5.2. Fermi Energy
10.5.3. Binding Energy
10.6. BLACK HOLES
10.6.1. Schwarzschild Radius
10.6.2. Hawking Radiation
10.7. THE DARK NIGHT SKY
10.8. HUBBLE’S LAW
10.8.1. Hubble Constant
10.8.2. Cosmic Redshift
10.9. COSMIC BACKGROUND RADIATION
10.10. COSMIC NEUTRINO BACKGROUND
10.11. CRITICAL MASS DENSITY
10.12. PLANCK MASS
10.12.1. Planck Length and Planck Time
10.12.2. Relationship to Schwarzschild Radius
APPENDIX A: Mathematica Starter
A.1. CELLS
A.2. PALETTES
A.3. FUNCTIONS
A.4. RESERVED NAMES
A.5. PHYSICAL CONSTANTS AND THEIR UNITS
A.6. INTEGRATION
A.6.1. Indefinite Integrals
A.6.2. Definite Integrals
A.6.3. Numerical Integration
A.6.4. Assumptions
A.7. RESOURCE FUNCTIONS
A.8. SERIES EXPANSION
A.9. SOLVING AN EQUATION
A.10. PLOTTING A FUNCTION
APPENDIX B: Physical Constants
Index
