Symmetry Theory in Molecular Physics with Mathematica

A New Kind of Tutorial Book
2008. Auflage 2014
ISBN: 978-1-4899-9518-6
Verlag: Springer

Buch, Englisch, 689 Seiten, Previously published in hardcover, Format (B × H): 156 mm x 234 mm, Gewicht: 1056 g

Prof. McClain has, quite simply, 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. It is aimed at 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 begins with the most elementary symmetry concepts, then presents mathematical group theory, and finally the projection operators that flow from the Great Orthogonality are automated and applied to chemical and spectroscopic problems.

Zielgruppe

Graduate

Autoren/Hrsg.

McClain, William

Fachgebiete

• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Chemie Physikalische Chemie Quantenchemie, Theoretische Chemie
• Naturwissenschaften Physik Quantenphysik Kernphysik
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Naturwissenschaften Physik Quantenphysik Atom- und Molekülphysik

Inhaltsverzeichnis

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.- Hybridorbitals.- 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.

Über Autor(innen)

W.M. McClain started working with Mathematica as soon as it appeared in 1988, bringing over ten years of nearly daily experience with Mathematica to this book.  He has written many research papers that use Mathematica and has also used group theory throughout his 20-year research career in nonlinear spectroscopy.  He published the first group theoretic analysis of nonlinear tensors in vibronic sprectroscopy, regarded by many as a landmark paper.