9. Harmonic Oscillator - MIT OpenCourseWare

← Back to document page

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.

consider a system with an infinite number of energy levels: the quantum harmonic oscillator (h.o.). The quantum h.o. is a model that describes systems with a characteristic energy spectrum, given by a ladder of evenly spaced energy levels. The energy difference between two consecutive levels is ∆E. The number of levels is

  Quantum, Mit opencourseware, Opencourseware