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Statistical Physics: relation to quanta and thermodynamics

سرفصل های دوره

The mathematics used in the discovery of quantum physics, the foundations of thermodynamics, phase transitions.


1 - Introduction
  • 1 - Introduction
  • 2 - Introduction to the blackbody problem
  • 3 - Definition of blackbody

  • 2 - Analysis of blackbody cavities
  • 4 - Irrelevance of Shape of the Cavity
  • 5 - Wave equation for Electromagnetic Waves
  • 6 - Solution to the Wave Equation
  • 7 - Compliance with Boundary Conditions
  • 8 - Number of Modes per Frequency
  • 9 - Average Energy per Mode

  • 3 - Quantization Systems of Particles
  • 10 - Distribution of the Average Energy Plancks idea
  • 11 - Systems of Particles Binomial Coefficient
  • 12 - Number of Arrangements of the Particles into the Energy Levels
  • 13 - Sterlings Approximation
  • 14 - Getting ready to maximize the Number of Arrangements

  • 4 - Derivation of the Average Energy per Mode
  • 15 - Maximizing the Number of Arrangements
  • 16 - Expression for the Energy per Mode
  • 17 - Plancks Mathematical Trick
  • 18 - Calculation of the Average Energy per Mode part 1
  • 19 - Calculation of the Average Energy per Mode part 2

  • 5 - Derivation of the StefanBoltzman Law
  • 20 - Classical vs Quantum
  • 21 - Energy per Volume per Wavelength and Energy per Volume
  • 22 - Plancks Integral
  • 23 - Brief Summary of Fourier Analysis
  • 24 - Parsevals Theorem
  • 25 - Ultraviolet Catastrophe and Energy per Unit Surface
  • 26 - Calculation of the Series 1n4
  • 27 - Putting Results Together
  • 28 - Deriving the StefanBoltzmann Law part1
  • 29 - Deriving the StefanBoltzmann Law part2

  • 6 - Useful appendix to the first part of the course
  • 30 - Derivation of the Maxwell Boltzmann distribution
  • 31 - Plancks idea for the mathematical solution to the black body problem
  • 32 - How Planck derived the blackbody radiation law the first time

  • 7 - Einsteins article on thermodynamics from 1902
  • 33 - The mathematics that Einstein used in one of his papers on thermodynamics part 1
  • 34 - The mathematics that Einstein used in one of his papers on thermodynamics part 2
  • 35 - The mathematics that Einstein used in one of his papers on thermodynamics part 3
  • 36 - The mathematics that Einstein used in one of his papers on thermodynamics part 4
  • 37 - The mathematics that Einstein used in one of his papers on thermodynamics part 5
  • 38 - Mathematical proof of Liouvilles theorem
  • 39 - Canonical transformations and generating functions
  • 40 - Hamilton equations derived from a variational principle
  • 41 - Variation principle derived from Newtons second law
  • 42 - Simple proof of Liouvilles theorem
  • 43 - Einsteins different approach for the derivation of the entropy
  • 44 - Ideal gas law derived from Statistical Mechanics

  • 8 - Einsteins article on the photoelectric effect which ushered in Quantum Physics
  • 45 - Part 1 of Einsteins article on the photoelectric effect
  • 46 - Part 2 of Einsteins article on the photoelectric effect
  • 47 - Part 3 of Einsteins article on the photoelectric effect
  • 48 - Part 4 of Einsteins article on the photoelectric effect

  • 9 - Einstein article on Brownian motion
  • 49 - stepbystep explanation of Einsteins article on the Brownian motion

  • 10 - Entropy derivation from Classical Mechanics
  • 50 - part 1 Entropy as a Function of State and How to Derive it from Lagrange Eqs
  • 51 - part 2 Entropy as a Function of State and How to Derive it from Lagrange Eqs
  • 52 - part 3 Entropy as a Function of State and How to Derive it from Lagrange Eqs

  • 11 - Phase transitions and the Ising model
  • 53 - Ising model and effective free energy
  • 54 - Mean field Theory in the Ising model
  • 55 - Landau approach to phase transitions
  • 56 - Discontinuity in the heat capacity
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    تاریخ انتشار: ۶ فروردین ۱۴۰۳
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