Mathematica is a powerful symbolic manipulator which provides very useful tools for solving problems and exploring the results. Its symbolic and graphical tools allow the student to focus more upon physics than upon algebra. A collection of notebooks has been prepared for several important topics and you are encouraged to use these notebooks as templates for the solution of other problems.

To view the notebooks without running Mathematica itself, you should obtain a copy of MathReader. We also offer a course entitled Essential Mathematica for Students of Science.

Most of these notebooks were originally written in 1996, but have been extensively revised in subsequent years; please check the dates to make sure that your copies are current. The present versions were prepared using Mathematica 4.0, but most should still run under Mathematica 3.0 with little or no change. Some notebooks may be temporarily unavailable, depending upon the choice of homework problems. For some notebooks postscript output is provided for students without access to Mathematica.

Last updated: Mar. 14, 2002

Lecture notes

ReviewThermodynamics     nb     pdf

Provides a brief review of thermodynamics and some of the techniques for derivation of thermodynamic relationships.
Revised Feb. 15, 2002.

StatisticalPostulate     nb     pdf

The basic postulates of statistical mechanics are used to derive and explain the laws of thermodynamics.  Our approach relies upon the information-theory concept of disorder and identifies the disorder within a statistical ensemble with thermodynamic entropy.
Revised Feb. 19, 2002.

Ensembles     nb     pdf

Two methods for construction of canonical probability distributions are presented.  The first is based upon thermal interaction between a sample and a much larger reservoir of heat.  The second maximizes entropy subject to constraints upon mean values of energy and perhaps other variables. 
Revised Mar. 14, 2002.

Semiclassical     nb     pdf

The properties of ensembles composed of points in classical phase space are studied.  Two important theorems, equipartition and virial, are developed.  Correspondence with quantum mechanics is used to establish a fundamental cell size in phase space that permits computation of finite entropy for semiclassical ensembles.  Applications are made to ideal gases and diatomic molecules.  
Revised Apr. 15, 2002.

Fluids     nb     pdf

The effects of intermolecular interactions upon the mechanical and thermal equations of state are studied for classical fluids.  The temperature dependence of the second virial coefficient, which governs these effects for dilute systems, is derived for realistic potentials and explained using a model from which one can also derive the van der Waals equation.  Next we discuss the measurement of the pair correlation function in denser systems using X-ray or neutron scattering.  Finally, the relationship between correlations and density fluctuations is developed. 
Revised Apr. 15, 2002.

IdealQuantumGases     nb     pdf

The indistinguishability of identical particles has profound effects at low temperatures and/or high densities where quantum mechanical wavepackets overlap appreciably.  The occupation representation is used to study the statistical mechanics and thermodynamics of ideal quantum gases satisfying Fermi-Dirac or Bose-Einstein statistics.  This notebook concentrates upon formal and conceptual developments, while the auxiliary notebook occupy.nb, fermi.nb, and bose.nb provide technical support. 
Revised Apr. 15, 2002.

 

Examples

stirling.nb

Derives an asymptotic expansion of the gamma function and investigates the accuracy of Stirling approximations.

binomial.nb

Investigates some of the properties of the binomial, Poisson, and Gaussian distributions.
Revised Jan. 11, 2000.

spin-half.nb

Uses the microcanonical ensemble to investigate the paramagnetism of spin-1/2 systems. The physical interpretation of the phenomenon of negative spin temperature is discussed in some detail.
Revised Jan. 11, 2000.

hotherm.nb

Uses the microcanonical ensemble to investigate the thermodynamics of independent oscillators. The Einstein model of lattice vibrations is presented.
Revised Jan. 11, 2000.

ising1d.nb

The combinatorial method is used to solve the Ising model for a one-dimensional chain of spin-1/2 atoms in an external magnetic field with nearest neighbor spin-spin interactions.
Revised Jan. 11, 2000.

Weiss.nb

Uses a mean-field model to study spontaneous magnetization for ferromagnetic systems, with particular attention to behavior near the critical point.
Revised Jan. 3, 2001.

thermo2.nb

Uses the canonical ensemble to investigate the thermodynamics of binary systems. The Schottky effect is discussed as a manifestation of the quantization of the excitation-energy spectrum.
Revised Jan. 11, 2000.

paramag.nb

Investigates the thermodynamics of paramagnetism for arbitrary spin using the canonical ensemble. The classical limit is developed also.
Revised Mar. 9, 2000.

debye.nb

Compares the Debye and Einstein models of lattice vibrations of a crystal. The Grueneisen model of expansivity is also developed.
Revised Mar. 9, 2000.

planck.nb

Compares the Planck model of black-radiation with earlier classical models. Also discusses Hawking radiation from black holes.
Revised Jan. 11, 2000.

rotvib.nb

Studies rotational and vibrational contributions to the heat capacity of ideal gases composed of diatomic molecules.
Revised Jan. 11, 2000

virial.nb

The second virial coefficient for classical gases is evaluated for realistic intermolecular potentials.
Revised Jan. 11, 2000

vdwaals.nb

Properties of the van der Waals gas, including the Maxwell construction, are developed.
Revised Jan. 11, 2000

occupy.nb

Investigates the statistics of occupation numbers for the Fermi-Dirac, Bose-Einstein, and Maxwell-Boltzmann distributions. The dependencies on both temperature and chemical potential are evaluated.
Revised Jan. 11, 2000

fermi.nb

Investigates the thermodynamics of ideal nonrelativistic Fermi-Dirac gases.
Revised Jan. 11, 2000

bose.nb

Investigates the thermodynamics of ideal nonrelativistic Bose-Einstein gases.
Revised Jan. 11, 2000