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  • 1
    UID:
    almahu_9947363656902882
    Format: XV, 689 p. , online resource.
    Edition: 1.
    ISBN: 9780387734705
    Content: 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 example of the enormous power of the automated projectors, the tensor operators for two- and three- photon processes are projected under all tabulated groups. All the machinery presented is general, and will work with new groups that you may construct. Finally, there is machinery that accepts as input the multiplication table of any group and returns as output its character table. This will be of great use to spectroscopists who deal with flexible molecules belonging to permutation groups, which are too numerous even for a Mathematica package.
    Note: 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.
    In: Springer eBooks
    Additional Edition: Printed edition: ISBN 9780387734699
    Language: English
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  • 2
    UID:
    b3kat_BV023029255
    Format: XV, 689 S. , Ill., graph. Darst. , 1 CD-ROM (12 cm)
    Edition: 1. ed.
    ISBN: 9780387734699 , 0387734694
    Language: English
    Subjects: Physics
    RVK:
    RVK:
    Keywords: Molekülphysik ; Symmetrie ; Mathematica
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  • 3
    UID:
    almahu_BV023029255
    Format: XV, 689 S. : , Ill., graph. Darst. , 1 CD-ROM (12 cm)
    Edition: 1. ed.
    ISBN: 978-0-387-73469-9 , 0-387-73469-4
    Language: English
    Subjects: Physics
    RVK:
    RVK:
    Keywords: Molekülphysik ; Symmetrie ; Mathematica
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  • 4
    UID:
    gbv_533207452
    Format: XV, 689 S , 50 schw.-w. Ill , 1 CD-ROM (12 cm) , 234 mm x 184 mm
    ISBN: 9780387734699 , 0387734694
    Content: "There is a paper version of this book and a CD ... version. The paper version is a reference work, providing most of the material on the CD. But you can put the CD into a computer and read the unabridged version from the screen, letting Mathematica recalculate all the results in the book as you go. If you do this, the Mathematica program will always be prepared to carry out experiments that are suggested in the text, or (even better) that you may think of on your own."--P. 3
    Additional Edition: ISBN 9780387734705
    Additional Edition: Erscheint auch als Online-Ausgabe McClain, William Martin, 1938 - Symmetry Theory in Molecular Physics with Mathematica New York, NY : Springer Science+Business Media, LLC, 2008 ISBN 9780387734705
    Additional Edition: ISBN 9781283438322
    Language: English
    Subjects: Physics
    RVK:
    RVK:
    Keywords: Molekülphysik ; Symmetrie ; Mathematica
    URL: Cover
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  • 5
    UID:
    kobvindex_ZLB15081360
    Format: 1 Buch (XV, 689 Seiten ), 1 CD-ROM , 234 mm x 184 mm
    Edition: 1
    ISBN: 9780387734699 , 9780387734705
    Note: Engl.
    Language: English
    Keywords: Mathematica 〈Programm〉
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