Lecture Notes CHEM 430b/530b
Statistical Methods and Thermodynamics
Prerequisites: CHEM 130 or 330 or 332, or equivalents
Instructor: Prof. Victor S. Batista
Room: SCL 18         Schedule: MWF 9.00-10.20


Introduction

 

(Chapter 3)
January 11-Feb 5

o   Pure States

o   Statistical Mixture of States

o   Density Operator

o   Time-Evolution of Ensembles

o   Classical Analogue

o   Entropy

o   Maximum-Entropy Density Operator

o   Internal Energy and Helmholtz Free Energy

o   Temperature

o   Canonical and Microcanonical Ensembles

o   Equivalency of Ensembles

§  Example

o   Thermal Fluctuations

o   Grand Canonical Ensemble

o   Density Fluctuations

§  Example

o   Quiz 1

o   Postulates of Statistical Mechanics

§  Example: Ensemble Averages

Practice Exam
Exam 1
 FIRST EXAM February 8th

(Chapter 4)
Febr. 8-25


February 10 don't meet

February
12, 15 meet at 9:00am

o   Bose-Einstein and Fermi-Dirac Distributions

o   Classical limit of Quantum Statistical Distributions

o   Example 1: Ideal Gas of Structureless Quantum Particles

o   Example 2: Dilute Gas of Diatomic Molecules

o   Example 3: Phonons in a Solid Lattice

§  Einstein Model

§  Debye Model

o   Example 4: Electrons in Metals

§  Continuous Approximation

§  Joint Probabilities

o   Chemical Equilibrium

§  Minimum Energy Principle

o   Practice Exam 2
Practice Quiz 2

(Chapter 5)
Febr. 25- March 5

February 22,24 don't meet

February 26, March 1, 3 and 5 meet at 9:00am

o   Ising Model

o   Lattice Gas

o   Mean Field Theory

§  Variational Mean Field Theory

o   Renormalization Group Theory 

SECOND EXAM  March 5

Spring Break March 6-21

 

(Chapter 6)

March 22-April 2

 

March 22, 31 don't meet

 

March 24, 26, 29 April 2 meet at 9:00am

o   Metropolis Monte Carlo Method

o   Variance-Reducing Techniques

§  Importance Sampling

§  Correlated Sampling

§  Control Variates

§  Stratified Sampling

§  Simulated Annealing

o   Practice Exam 3

o   Kinetic Monte Carlo

(Chapters 7 and 8)

April 7-16

April 9 don't meet

 

April 12, 14 meet at 9:00am

o   Classical Fluids

§  Radial Distribution Function

o   Reversible Work Theorem

o   Thermodynamic Properties of Fluids

o   Solvation Free Energy

Quiz 3
April 18: Computer assignments deadline

DEADLINE COMPUTER ASSIGNMENTS  April 16

(Chapter 8)

April 19-30

April 26-30 (reading period) meet

 

THIRD EXAM  April 30

FINAL EXAMINATION PERIOD MAY 4-11

            OPTIONAL COMPREHENSIVE MAKEUP EXAM,  May 7