The Harmonic Oscillator
In this section I will put the hamwnic oscillator in its place-on a pedestaL Not only is it a system that can be exactly solved (in classical and quantum theory) and a superb pedagogical tool (which will be repeatedly exploited in this text), but it is also a system of great physical relevance. As will be shown below, any system fluctuating by small amounts near a configuration of stable equilibrium may be described either by an oscillator or by a collection of decoupled harmonic oscillators. Since the dynamics of a collection of noninteracting oscillators is no more complicated than that of a single oscillator (apart from the obvious N-fold increase in degrees of freedom), in addressing the problem of the oscillator we are actually confronting the general problem of small oscillations near equilibrium of an arbitrary system.
KeywordsNormal Mode Harmonic Oscillator Poisson Bracket Recursion Relation Eigenvalue Equation
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