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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تولید کننده: Udemy