Transcription of 9. Harmonic Oscillator - MIT OpenCourseWare
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9. Harmonic Oscillator - MIT OpenCourseWare
9. Harmonic Oscillator Harmonic Oscillator Classical Harmonic Oscillator and model Oscillator Hamiltonian: Position and momentum operators Position representation Heisenberg picture Schro dinger picture Uncertainty relationships Coherent States Expansion in terms of number states Non-Orthogonality Uncertainty relationships X-representation Phonons Harmonic Oscillator model for a crystal Phonons as normal modes of the lattice vibration Thermal energy density and Specific Heat Harmonic Oscillator We have considered up to this moment only systems with a finite number of energy levels; we are now going to consider a system with an infinite number of energy levels: the quantum Harmonic Oscillator ( ). The quantum is a model that describes systems with a characteristic energy spectrum, given by a ladder of evenly spaced energy levels.
9.4.1 Harmonic oscillator model for a crystal We have considered up to this moment only systems with a finite number of energy levels; we are now going to consider a system with an infinite number of energy levels: the quantum harmonic oscillator (h.o.).
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