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Quantum Theory of Anharmonic Effects in Molecules

By
  • Konstantin Kazakov, Irkutsk, Russia

Presented in a clear and straightforward analysis, this book explores quantum mechanics and the application of quantum mechanics to interpret spectral phenomena. Specifically, the book discusses the relation between spectral features in mid or rear infrared regions, or in Raman scattering spectrum, and interactions between molecules or molecular species such as molecular ions, and their respective motions in gaseous or crystalline conditions. Beginning with an overview of conventional methods and problems which arise in molecular spectroscopy, the second half of the book suggests original techniques to investigate the area. The treatment is based on rigorous quantum-mechanical theories and procedures that are readily implemented in either manual methods or with symbolic computational software.

Hardbound, 232 Pages

Published: July 2012

Imprint: Elsevier

ISBN: 978-0-12-397912-4

Contents

  • Chapter 1 - The Laws of Quantum Mechanics

    1. Introduction

    • Observables and variables
    • The conditions of quantum theory
    • Angular momentum

    2. The principal equations

    • Dirac’s theory

    3. Spin and magnetic moment

    • Phenomenological description

    4. Semiclassical theory of radiation

    • Fermi’s golden rule
    • Intensities of transitions

    5. Second quantization

    • An harmonic oscillator
    • The fields of bosons and fermions

    6. Molecules

    • Born-Oppenheimer approximation
    • Chemical bond

    7. Questions of symmetry

    • Point groups
    • Classification of states according to symmetry

    Chapter 2 - The Evolution of Perturbation Theory

    1. Preamble

    • Frequencies and intensities

    2. Perturbation algebra

    • Expansions of two types
    • Many-time formalism

    3. Methods of quantum-field theory

    • Diagrams and computational rules

    4. Other trends and methods

    • Alternative perturbation theory
    • Canonical transformation
    • Hypervirial result

    Chapter 3 - Polynomials of Quantum Numbers

    1. The principles of the theory

    • Recurrence equations
    • Many-dimensional case
    • The problem of degenerate states
    • Introduction to a theory of anharmonicity

    2. Advantages of the new technique

    • Polynomials and computational rules

    3. Electro-optics of molecules

    • Phenomenon of strong anharmonicity
    • The direct and inverse problems of spectroscopy

    4. Extraneous quantum numbers

    • Factorization of the matrix elements
    • The first coefficients
    • Calculation of higher-order approximations

    5. Future developments

    • Functions of quantum numbers

    6. Background

    Chapter 4 - Effects of Anharmonicity

    1. Extension to magnetic phenomena

    • Magneto-optical anharmonicity

    2. Electron in a magnetic field

    3. The resonance interaction

    • Dimers in low-temperature liquids

    4. Diatomic dimers

    • On the theory of overtones
    • XH-XH pairs

    Chapter 5: The Method of Factorization

    1. Algebraic formalism

    Atom of hydrogen type

    2. Some problems involving anharmonicity

    Poschl - Teller potential

    Poschl - Teller-like potential

    Morse's oscillator

    Generalized Morse's oscillator

    REFERENCES

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