STATISTICAL AND SOLID STATE PHYSICS

Paper Code: 
PHY 224
Credits: 
4
Contact Hours: 
60.00
Max. Marks: 
100.00
Objective: 

This course will enable the students to –

  1. To provide knowledge of Partition functions, Statistics, Band Theory  of solids to solve to various types of applications and problems
  2. To make students able to apply knowledge acquired from this paper to realistic problems of Condensed Matter and Solid State Physics.

 

Course outcomes (COs):

                     Course

Learning outcome (at course level)

Learning and teaching strategies

Assessment Strategies

Paper Code

Paper Title

PHY 224

Statistical 

The students will be able to –

 

CO 63: Have a brief idea about basic principles and applications of Canonical and Grand Canonical ensembles.

 

CO 64: Have a knowledge of Partition functions, Statistics, partition function for an ideal gas and calculation of thermodynamic quantities, partition function and Specific heat of an ideal diatomic gas.

 

 

CO 65: Understand the difficulties with Maxwell-Boltzmann statistics.

 

CO 66: Discuss  quantum distribution functions like Bose Einstein and Fermi-Dirac statistics and apply them to derive Planck's formula, Bose Einstein condensation.

 

 

CO 67:  Know about quantization of harmonic oscillator and Fermion operators, creation and annihilation of phonon operators.

 

CO 68: Understand the basic idea about Theory of Metals, use of Fermi-Dirac statistics in the calculation of thermal conductivity and electrical conductivity, Drude theory of light, absorption in metals.

 

 

CO 69: Have basic knowledge of  band theory  ,Bloch theorem, K.P. model, NFE model, tight binding method ,application to simple cubic lattice and pseudo-potential method.

 

 

Approach in teaching:

Interactive Lectures, Discussion, Tutorials, , Demonstration, Problem Solving in tutorials

 

 

 

 

 

 

 

Learning activities for the students:

Self learning assignments, Effective questions,  Seminar presentation, Solving numericals.

Additional learning through online videos and MOOC courses.

Class test, Semester end examinations, Quiz, Solving problems, Assignments, Presentations

 

13.00
Unit I: 
Basic Principles, Canonical and Grand Canonical ensembles
Concept of statistical distribution, phase space, density of states ,Liouville's theorem, systems and ensemble, entropy in statistical mechanics, Connection between thermodynamic and statistical quantities, micro canonical ensemble, equation of state, specific heat and entropy of a perfect gas using microcanonical ensemble.
Canonical ensemble, thermodynamic functions for the canonical ensemble, calculation of mean value, energy fluctuation in a gas, grand canonical ensemble, thermodynamic functions for the grand canonical ensemble, density fluctuations.
                                                          
11.00
Unit II: 
Partition functions and Statistics
Partition functions and properties, partition function for an ideal gas and calculation of thermodynamic quantities, Gibbs Paradox, validity of classical approximation, determination of translational, rotational and vibration contributions to the partition function of an ideal diatomic gas. Specific heat of a diatomic gas, ortho and para hydrogen.
                                                             
13.00
Unit III: 
III
Identical particles and symmetry requirement, difficulties with Maxwell-Boltzmann statistics, quantum distribution functions, Bose Einstein and Fermi-Dirac statistics and Planck's formula, Bose Einstein condensation, liquid He4 as a Boson system, quantization of harmonic oscillator and creation and annihilation of phonon operators, quantization of fermion operators.
                                                       
11.00
Unit IV: 
Theory of Metals
Fermi-Dirac distribution function, density of states, temperature dependence of Fermi energy, specific heat, use of Fermi-Dirac statistics in the calculation of thermal conductivity and electrical conductivity, Drude theory of light, absorption in metals. 
 
 
 
12.00
Unit V: 
Band Theory

Bloch theorem, Kroning Penny model, effective mass of electrons, Wigner-Seitz approximation, NFE model, tight binding method and calculation of density for a band in simple cubic lattice, pseudo potential method.

BOOKS RECOMMENDED:

  • “Statistical Mechanics “,Huag
  • ” Fundamentals of Statistical and Thermodynamical Physics”, Reif.
  •  “Statistical mechanics and Thermal Physics”, Rice
  •  “Elementray statistical mechanics”, Kittle.
  •  “Introduction to solid state physics”. Kittle
  •  “Solid State Physics”. Palteros
  •  “Solid State Physics.” Levy

 

References: 
 
 
 
Academic Year: 
2020-2021
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