Statistical Mechanics

  • Course level: Intermediate


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 – low-density 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 Micro-canonical

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:Real-Particle Ideal Gas (Fermions & Bosons)

Week 11:Metals and Electrons

Week 12:Quantum Gases’ Classical Limit

Topics for this course

34 Lessons

Lecture 01-Discrete Probability

Lecture 02-Continous Probability00:47:08
Lecture 03 Characteristic Function00:44:43
Lecture 04-Gausssian Distribution00:38:46
Lecture 05-Binomial Distribution00:46:31
Lecture 06-Poisson Distribution00:46:45
Lecture 07-Central Limit Theorem00:48:00
Lecture 08-Many Random Variables00:39:20
Lecture 09-Entropy and Probability00:58:47
Lecture 10-Entropy Maximization00:37:43
Lecture 11-Transformation of Random Variable00:43:53
Lecture 12-Tutorial00:47:38
Lecture 13-Mathematical Preliminaries 100:58:15
Lecture 14-Microcanonical Ensemble01:06:14
Lecture 15-Two Level System (Microcanonical Ensemble)00:44:34
Lecture 16-Classical Ideal Gas (Microcanonical Ensemble)00:52:09
Lecture 17-Entropy of Mixing01:03:03
Lecture 18-Classical Ideal Gas (Canonical Ensemble)01:06:29
Lecture 19-Gibbs Canonical Ensemble00:45:19
Lecture 20-Canonical Ensemble00:35:24
Lecture 21-Classical Ideal Gas (Gibbs Canonical Ensemble)00:48:05
Lecture 22-Two Level System (Canonical Ensemble)01:06:09
Lecture 23-N Spins in a Uniform Magnetic Field00:27:05
Lecture 24-Grand Canonical Ensemble00:46:45
Lecture 25-Ideal Gas (Grand Canonical Ensemble)00:42:35
Lecture 26-N Non – Interacting Spins in Constant Magnetic Field01:06:06
Lecture 27-Quantum statistical mechanics01:05:56
Lecture 28-Statistics of Fermions and Bosons00:46:57
Lecture 29-Quantum to Classical Correspondance01:02:21
Lecture 30-Vibrations of Solid (Low Temperature)01:11:30
Lecture 31-Vibrations of Solid (Continuation)00:50:02
Lecture 32 Free Electrons(Fermi Gas) in a Metal00:43:09
Lecture 33 Free Electrons(Fermi Gas) in a Metal(Continuation)01:32:55
Lecture 34 – Problem solving demo – part 100:57:08
Lecture 35 – Problem solving demo – part 200:34:55

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Very informative and deep technical course


Enrolment validity: Lifetime