Algebraic Theory of Molecules
Algebraic Theory of Molecules presents a fresh look at the mathematics of wave functions that provide the theoretical underpinnings of molecular spectroscopy. Written by renowned authorities in the field, the book demonstrates the advantages of algebraic theory over the more conventional geometric approach to developing the formal quantum mechanics inherent in molecular spectroscopy. Many examples are provided that compare the algebraic and geometric methods, illustrating the relationship between the algebraic approach and current experiments. The authors develop their presentation from a basic level so as to enable newcomers to enter the field while providing enough details and concrete examples to serve as a reference for the expert. Chemical physicists, physical chemists, and spectroscopists will want to read this exciting new approach to molecular spectroscopy.
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Chapter 1 The Wave Mechanics of Diatomic Molecules
Chapter 2 Summary of Elements of Algebraic Theory
Chapter 3 Mechanics of Molecules
Chapter 4 Threebody Algebraic Theory
Chapter 5 FourBody Algebraic Theory
Chapter 6 ManyBody Algebraic Theory
Chapter 7 Classical Limit and Coordinate Representation
Chapter 8 Prologue to the Future
Properties of Lie Algebras
Coupling of Algebras
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alge algebraic approach algebraic Hamiltonian algebraic theory Alhassid angular momentum anharmonic approximation atoms basis bending vibrations benzene bilinear bonds boson operators calculation Casimir invariant Casimir operators chain Chapter characterized Computed coordinates corresponding cºs denote described diagonal diatomic dynamical symmetry eigenvalues energy levels evaluated example expectation value Fermi geometrical given by Eq Hamiltonian operator harmonic limit harmonic oscillator Higher-order Iachello infrared integers introduce Lemus Levine Lie algebras linear molecules linear triatomic molecules local-mode Majorana operator matrix elements modes molecular momenta Morse functions Morse oscillator Morse potential multiplet notation obtained one-dimensional problems orthogonal overtones parameters potential function previous sections quantum mechanics recoupling coefficients representations resonance Roosmalen rotation—vibration interactions rotational rovibrator Schrödinger equation shown in Figure spectra spectroscopy spectrum spherical stretching vibrations subalgebra Table tensor tion transformation variables vector vibrational quantum numbers vibron numbers wave functions written in terms