Transcription of Harmonic oscillator Notes on Quantum Mechanics
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Harmonic oscillator Notes on Quantum Mechanics
Harmonic oscillatorNotes on Quantum updated Thursday, November 30, 2006 13:50:03-05:00 Copyright 2006 Dan Dill of Chemistry, Boston University, Boston MA 02215 Classical Harmonic motionThe Harmonic oscillator is one of the most important model systems in Quantum Mechanics . An Harmonic oscillator is a particle subject to a restoring force that is proportional to the displacement of the particle. In classical physics this meansF=ma=m 2x t2=-kxThe constant k is known as the force constant; the larger the force constant, the larger the restoring force for a given displacement from the equilibrium position (here taken to be x=0). A simple solution to this equation is that the displacement x is given byx=sinI !!!!!!!!!!k m tM,sincem 2x t2=m 2 t2 sinI !!!!!!!!!!k m tM=-mI !!!!!!!!!!k mM2 sinI !
The harmonic oscillator is one of the most important model systems in quantum mechanics. An harmonic oscillator is a particle subject to a restoring force that is proportional to the displacement of the particle. In classical physics this means F =ma=m
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