About Course
Statistical Mechanics
The course is meant to provide advanced undergraduate/beginning graduate students with a solid understanding of statistical mechanics. Following a review of probability principles, the classical postulates are presented.
Mechanics are developed in a variety of physical ensembles. The classical ideas that arose as a result of this process When used, systems will be proven to have significant limits.
As a result, ideas for the classical period arose. When applied to quantum systems, systems will be demonstrated to have major limitations. Finally, we create the appropriate show that classical outcomes can be retrieved from the theory of statistical mechanics for quantum systems the high temperature – lowdensity limit, quantum theories are used.
Course plan
Week 01:Random Variables
Week 02: Cumulants & Moments
Week 03: Important Probability Distributions
Week 04:The principle of maximum entropy
Week 05:Ensemble Microcanonical
Week 06:Canonical Ensemble
Week 07:Gibbs Canonical Ensemble
Week 08:The Canonical Grand Ensemble
Week 09:Particles with no mass form an ideal gas (Photons & Phonons)
Week 10:RealParticle Ideal Gas (Fermions & Bosons)
Week 11:Metals and Electrons
Week 12:Quantum Gases’ Classical Limit
Course Content
Lecture 01Discrete Probability

Lecture 02Continous Probability
47:08 
Lecture 03 Characteristic Function
44:43 
Lecture 04Gausssian Distribution
38:46 
Lecture 05Binomial Distribution
46:31 
Lecture 06Poisson Distribution
46:45 
Lecture 07Central Limit Theorem
48:00 
Lecture 08Many Random Variables
39:20 
Lecture 09Entropy and Probability
58:47 
Lecture 10Entropy Maximization
37:43 
Lecture 11Transformation of Random Variable
43:53 
Lecture 12Tutorial
47:38 
Lecture 13Mathematical Preliminaries 1
58:15 
Lecture 14Microcanonical Ensemble
01:06:14 
Lecture 15Two Level System (Microcanonical Ensemble)
44:34 
Lecture 16Classical Ideal Gas (Microcanonical Ensemble)
52:09 
Lecture 17Entropy of Mixing
01:03:03 
Lecture 18Classical Ideal Gas (Canonical Ensemble)
01:06:29 
Lecture 19Gibbs Canonical Ensemble
45:19 
Lecture 20Canonical Ensemble
35:24 
Lecture 21Classical Ideal Gas (Gibbs Canonical Ensemble)
48:05 
Lecture 22Two Level System (Canonical Ensemble)
01:06:09 
Lecture 23N Spins in a Uniform Magnetic Field
27:05 
Lecture 24Grand Canonical Ensemble
46:45 
Lecture 25Ideal Gas (Grand Canonical Ensemble)
42:35 
Lecture 26N Non – Interacting Spins in Constant Magnetic Field
01:06:06 
Lecture 27Quantum statistical mechanics
01:05:56 
Lecture 28Statistics of Fermions and Bosons
46:57 
Lecture 29Quantum to Classical Correspondance
01:02:21 
Lecture 30Vibrations of Solid (Low Temperature)
01:11:30 
Lecture 31Vibrations of Solid (Continuation)
50:02 
Lecture 32 Free Electrons(Fermi Gas) in a Metal
43:09 
Lecture 33 Free Electrons(Fermi Gas) in a Metal(Continuation)
01:32:55 
Lecture 34 – Problem solving demo – part 1
57:08 
Lecture 35 – Problem solving demo – part 2
34:55