## The Bell that Rings Light: A Primer in Quantum Mechanics and Chemical Bonding"This book is an introduction to quantum mechanics and mathematics that leads to the solution of the Schrodinger equation. It can be read and understood by undergraduates without sacrificing the mathematical details necessary for a complete solution giving the shapes of molecular orbitals seen in every chemistry text. Readers are introduced to many mathematical topics new to the undergraduate curriculum, such as basic representation theory, Schur's lemma, and the Legendre polynomials."--Back cover. |

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### Contents

Rutherford Bohr and Balmer | 1 |

Some Important Experiments | 7 |

The Atom | 15 |

New Assumptions | 19 |

Zetetics | 23 |

Classical Waves | 31 |

ParticleinaBox | 39 |

Exploring the Analogy | 45 |

More French Mathematicians | 71 |

The Quantum Numbers | 77 |

Chemistry and Bonding | 81 |

Valence Shell Electron Pair Repulsion | 89 |

The Shape of an Orbital | 93 |

Molecular Orbital Theory | 103 |

Valence Bond Theory | 117 |

Other Kinds of Bonding | 123 |

### Common terms and phrases

2p orbital actually angular assumptions atomic orbitals axis Balmer blackbody Bohr bond angle bond energy Bond order bonding orbital called carbon Chapter charge chemical chemistry classical physics coefficients combine compute constant corresponding Coulomb's Law derived describe differential equations eigenfunction eigenvalue problem electron configuration energy level example experimental exponential Figure Fourier frequency geometry given harmonic hybrid orbitals hydrogen atom hydrogen bonding interactions Legendre polynomial Lewis dot structure light look mathematical mathematician matrix molecular molecules momentum node nucleus object observed octet rule one-dimensional operator oscillation particle particle-in-a-box physicists position possible potential energy power series principal quantum principal quantum number probability density probability distribution proton quantum mechanics radiation representation result rotations Schematic Schrodinger equation Schrodinger's equation Schur's lemma shown in Fig solution to Schrodinger's solve space of functions spectrum sphere spherical subspaces symmetry tion vector space vibrating string VSEPR wave equation wavefunction wavelength zero