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The harmonic oscillator is extremely useful in chemistry as a model for the vibrational motion in a diatomic molecule. Polyatomic molecules can be modeled by coupled harmonic oscillators. The atoms are viewed as point masses which are connected by bonds which act (approximately) like springs obeying Hooke's law. In these notes we will review the classical harmonic oscillator problem and then discuss the quantum harmonic oscillator.

David Sherrill 2002-10-16