








Symmetry Theory in Molecular Physics with Mathematica: A New Kind of Tutorial Book






Organization:  Wayne State University 
Department:  Department of Chemistry 






Publisher:  Springer (New York, NY) 
Additional cataloguing information:  ISBN10: 0387734694 
  






Introduction  A Tutorial on Notebooks  A Basic Mathematica 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's AxisAngle Rotations  Recognizing Matrices  Introduction to the Character Table  The Operator MakeGroup  Product Groups  Naming the Point Groups  Tabulated Representations of Groups  Visualizing Groups  Subgroups  Lagrange's Theorem  Classes  Symmetry and Quantum Mechanics  Transformation of Functions  Matrix Representations of Groups  Similar Representations  The MakeRep Operators  Reducible Representations  The MakeUnity Operator  Schur's Reduction  Schur's First Lemma  Schur'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  OnePhoton Selection Rules  TwoPhoton Tensor Projections  ThreePhoton Tensor Projections  Class Sums and Their Products  Make a Character Table  Appendices






After a few initial chapters on the basics of Mathematica, the logic of this book is controlled by group theory. 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, before moving on to the construction of mathematical groups. In Part II, mathematical group theory is presented with motivating questions and experiments first, and theorems that answer those questions second. 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. Intended for students of chemistry and molecular physics, the book may be read either independently or on a computer screen with Mathematica running behind it. The included CDROM presents the entire content of the book plus interactive examples using Mathematica notebooks for problemsolving and learning.












Cartesian representation, character table, group theory, subgroups, symmetry, molecules, point groups, representation theory, Schur's lemma, Issai Schur, Great Orthogonality







   
 
