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Statistical Physics Using Mathematica

James J. Kelly
Organization: University of Maryland
Department: Department of Physics
Education level


Develop the basic principles of equilibrium statistical mechanics and their application to the thermodynamics of a wide variety of physical systems.

All required materials and a list of useful references may be found at the URL below.

We offer a large collection of Mathematica notebooks used in a graduate course on equilibrium statistical mechanics. Two types of notebooks are provided:
  • Formalism notebooks use the typesetting capabilities to present the theoretical development of the subject in a format similar to a traditional deadtree textbook.
  • Application notebooks provide the Mathematica code used to derive many of the symbolic results and to perform the numerical work needed to produce figures and to solve nontrivial problems.
    Using these methods a student becomes empowered to solve a much broader range of problems than is possible with traditional pen-and-paper methods.

    Traditional physics education tends to limit its choice of problems to those which a clever mathematician can solve in symbolic form, but modern research depends upon computational tools. Even if a symbolic solution is possible, it is often very difficult to produce accurate sketches of the dependencies of various thermodynamic properties upon the relevant variables without the assistance of a computer program. Although such plots are essential to the development of understanding and physical insight, few students can produce realistic sketches unaided. In fact, most instructors reproduce on the blackboard figures produced by computers and then imply that students should achieve comparable accuracy without such assistance. Recognizing the folly of this expectation, we provide tools to assist students in solving problems and exploring the meaning of their solutions.

  • Thermodynamics
  • Postulates of Statistical Mechanics
  • Canonical Ensembles
  • Semiclassical methods
  • Pair correlation in fluids
  • Ideal Quantum Gases
  • Ising model
  • Subject

    *Science > Physics > Thermodynamics and Statistical Mechanics
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