✎ Harmonic Oscillator [The Physics Travel Guide]

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====== Harmonic Oscillator ======

<blockquote>“The career of a young theoretical physicist consists of treating the harmonic
oscillator in ever-increasing levels of abstraction.” <cite>Sidney Coleman</cite></blockquote>

<blockquote>In a sense, the harmonic oscillator is to physics what the set of natural numbers
is to mathematics. It is a simple, almost “trivial” system, but one which conceals
much subtlety and beauty and from which a great deal of what is of interest in the
subject evolves. <cite>[[http://gregnaber.com/wp-content/uploads/Simple-Harmonic-Oscillator.pdf|Gregory L. Naber]]</cite></blockquote>

<blockquote>The harmonic oscillator is an important model system pervading many areas
in classical physics; it is likewise ubiquitous in quantum mechanics. The nonrelativistic
Scrodinger equation with a harmonic oscillator potential is readily ¨
solved with standard analytic methods, whether in one or three dimensions.
However, we will take a different tack here, and address the one-dimension
problem more as an excuse to introduce the notion of “creation” and “annihilation”
operators, or “step-up” and “step-down” operators. This is an
example of a type of operation which will repeat itself in many contexts,
including the theory of angular momentum.

<cite>[[http://www.hep.caltech.edu/~fcp/physics/quantumMechanics/SHO/SHO.pdf|The Simple Harmonic Oscillator]] by F. Porter</cite></blockquote>
<tabbox Layman>

<note tip>
Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party.
</note>
  
<tabbox Student> 
  * A good description can be found at http://www.hep.caltech.edu/~fcp/physics/quantumMechanics/SHO/SHO.pdf

--> Example1#

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--> Example2:#

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<tabbox FAQ>

--> Why do we introduce the ladder operators?#

* See https://behindtheguesses.blogspot.de/2009/03/quantum-harmonic-oscillator-ladder.html

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</tabbox>

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