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Related Experiment Videos

Extended Watson integrals for the cubic lattices.

M L Glasser1, I J Zucker

  • 1Quantum Theory Group, Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada.

Proceedings of the National Academy of Sciences of the United States of America
|May 1, 1977
PubMed
Summary

This study summarizes exact expressions for extended Watson integrals in cubic lattices. A novel closed-form expression for the simple cubic lattice is presented using gamma functions.

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Area of Science:

  • Mathematical Physics
  • Condensed Matter Theory

Background:

  • Extended Watson integrals are crucial in statistical mechanics and lattice sums.
  • Previous work established expressions for various cubic and modified cubic lattices.

Purpose of the Study:

  • To consolidate known exact expressions for extended Watson integrals.
  • To derive a new closed-form expression for the simple cubic lattice.

Main Methods:

  • Literature review and summarization of existing formulas.
  • Derivation of a new expression using mathematical identities and gamma functions.

Main Results:

  • Compilation of known exact expressions for extended Watson integrals.
  • Presentation of a novel closed-form expression for the simple cubic lattice in terms of gamma functions.

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Conclusions:

  • The study provides a comprehensive summary of existing integral expressions.
  • The new expression simplifies calculations for the simple cubic lattice, aiding further research in lattice physics.