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### Summary

### Summary

This text presents a rigorous mathematical account of the principles of quantum mechanics, in particular as applied to chemistry and chemical physics. Applications are used as illustrations of the basic theory. The first two chapters serve as an introduction to quantum theory, although it is assumed that the reader has been exposed to elementary quantum mechanics as part of an undergraduate physical chemistry or atomic physics course. Following a discussion of wave motion leading to Schrdinger's wave mechanics, the postulates of quantum mechanics are presented along with essential mathematical concepts and techniques. The postulates are rigorously applied to the harmonic oscillator, angular momentum, the hydrogen atom, the variation method, perturbation theory, and nuclear motion. Modern theoretical concepts such as hermitian operators, Hilbert space, Dirac notation, and ladder operators are introduced and used throughout. This text is appropriate for beginning graduate students in chemistry, chemical physics, molecular physics and materials science.

### Reviews 1

### Choice Review

Is there the need for another book on introductory quantum mechanics? The topics that are covered are almost always the same, so the case for a new book must rest with the approach and point of view of the author. The topics in Fitts's book are much the same as one finds in Linus Pauling and E. Bright Wilson's Introduction to Quantum Mechanics, first published in 1935. The difference is the emphasis and style. Traditional texts generally begin with partial differential equations that are solved using series solution methods; Fitts (Univ. of Pennsylvania) takes an intermediate approach, using series solutions for some systems and solving others, such as the harmonic oscillator, with more up-to-date operator methods. The discussion in chapter 1 of the superposition of waves and of wave packets provides the background for Schr"odinger wave mechanics introduced in chapter 2. The following chapters treat one-, two-, and three-dimensional systems as well as approximation methods, systems of particles, and diatomic molecules. The point of view is formal and rigorous, with some examples from chemistry and chemical physics. The clarity of the presentation will be appreciated by those with some prior exposure to quantum mechanics. Upper-division undergraduate and graduate students. M. Coplan; Institute for Physical Science and Technology

### Table of Contents

1 The wave function |

2 SchrÃ¶dinger wave mechanics |

3 General principles of quantum theory |

4 Harmonic oscillator |

5 Angular momentum |

6 Hydrogen atom |

7 Spin |

8 Systems of identical particles |

9 Approximation methods |

10 Molecular structure |

Appendix A Mathematical formulas |

Appendix B Fourier series and Fourier integral |

Appendix C Dirac delta function |

Appendix D Mermite polynomials |

Appendix E Legendre and associated Legendre polynomials |

Appendix F Laguerre and associated Laguerre polnomials |

Appendix G Series solutions of differential equations |

Appendix H Recurrence relation for hydrogen-atom expectation values |

Appendix I Matrices |

Appendix J Evaluation of two-electron interaction integral |