rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Symmetry Theory in Molecular Physics with Mathematica
    sub title: A new kind of tutorial book
  name:
    name part: McClain, William.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2008
    edition: 1.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XV, 689 p. online resource.
  abstract: Prof. McClain has indeed produced "a new kind of tutorial book." It is written using the logic engine Mathematica, which permits concrete exploration and development of every concept involved in Symmetry Theory. The book may be read in your hand, or on a computer screen with Mathematica running behind it. It is intended for students of chemistry and molecular physics who need to know mathematical group theory and its applications, either for their own research or for understanding the language and concepts of their field. The book has three major parts: Part I begins with the most elementary symmetry concepts, showing how to express them in terms of matrices and permutations. These are then combined into mathematical groups. Many chemically important point groups are constructed and kept in a Mathematica package for easy reference. No other book gives such easy access to the groups themselves. The automated group construction machinery allows you to tabulate new groups that may be needed in research, such as permutation groups that describe flexible molecules. In Part II, mathematical group theory is presented with motivating questions and experiments coming first, and theorems that answer those questions coming second. You learn to make representations of groups based on any set of symmetric objects, and then to make Mathematica operators that carry out rep construction as a single call. Automated construction of representations is offered by no other book. Part II follows a reconstructed trail of questions, clues and solid results that led Issai Schur to a complete proof of the Great Orthogonality. In Part III, the projection operators that flow from the Great Orthogonality are automated and applied to chemical and spectroscopic problems, which are now seen to fall within a unified intellectual framework. The topics include chemical bonding in symmetric molecules, molecular vibrations and rigorous reasoning about quantum mechanical matrix elements. As a concrete e…
  table of contents: A tutorial on notebooks -- A basic tutorial -- The meaning of symmetry -- Axioms of group theory -- Several kinds of groups -- The fundamental theorem -- The multiplication table -- Molecules -- The point groups -- Euler rotation matrices -- Lie#x2019;s axis-angle rotations -- Recognizing matrices -- to the character table -- The operator MakeGroup -- Product groups -- Naming the point groups -- Tabulated representations of groups -- Visualizing groups -- Subgroups -- Lagrange#x2019;s Theorem -- Classes -- Symmetry and quantum mechanics -- Transformation of functions -- Matrix representations of groups -- Similar representations -- The MakeRep operators -- Reducible representations -- The MakeUnitary operator -- Schur#x2019;s reduction -- Schur#x2019;s First Lemma -- Schur#x2019;s Second Lemma -- The Great Orthogonality -- Character orthogonalities -- Reducible rep analysis -- The regular representation -- Projection operators -- Tabulated bases for representations -- Quantum matrix elements -- Constructing SALCs -- Hybrid orbitals -- Vibration analysis -- Multiple symmetries -- One-photon selection rules -- Two-photon tensor projections -- Three-photon tensor projections -- Class sums and their products -- Make a character table.
  note: by William McClain.
  subject:
    topic: Physics
  subject:
    topic: Physical chemistry
  subject:
    topic: Chemistry, Physical and theoretical
  subject:
    topic: Group theory
  subject:
    topic: Nuclear physics
  subject:
    topic: Atomic structure
  subject:
    topic: Molecular structure
  subject:
    topic: Spectra
  subject:
    topic: Physics
  subject:
    topic: Particle and Nuclear Physics
  subject:
    topic: Theoretical and Computational Chemistry
  subject:
    topic: Theoretical, Mathematical and Computational Physics
  subject:
    topic: Group Theory and Generalizations
  subject:
    topic: Physical Chemistry
  subject:
    topic: Atomic/Molecular Structure and Spectra
  classification: QC770-798
  classification: 539.7
  related item:
    title info:
      title: Springer eBooks
  identifier: 9780387734705
  identifier: http://dx.doi.org/10.1007/b13137
  record info:
    record creation date: 100715
    record change date: 20151204165306.0
    record identifier: 978-0-387-73470-5