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### Contents

Harmonic oscillators | 13 |

Field quantization | 49 |

classical | 61 |

Copyright | |

33 other sections not shown

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### Common terms and phrases

amplitudes analogy annihilation operators apply assume Bose operators calculate charge density classical co-ordinates coefficients commutation relations conduction band conjugate momentum constant continuum corresponding Coulomb interaction creation and annihilation creation operators crystal derive describes dipole effective mass eigenfunctions electron and hole emission equation of motion evaluate example exciton Exercise expansion expectation value explicit form exponential function expression factor Fermi final Frenkel excitons given Green's function Hamiltonian operator Heisenberg picture hole operators initial integrate with respect interaction between electrons interaction energy Lagrangian lattice vibrations left-hand side let us consider method multiply normalization obtain the following perturbation theory phonon plane waves polarization polarons potential energy problem quantum field theory quantum mechanics replaced result right-hand side satisfy Schrodinger equation second quantization self-energy solution solve substitute suffices sum with respect superconductivity time-dependent valence band Wannier functions wave field wave function wave vector zero