The simple harmonic oscillator in quantum mechanics -- Jacob Aaron Barandes, April 27, 2004

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The simple harmonic oscillator is much more than simply 
a useful approximation to classical and quantum mechanical 
systems near points of equilibrium. After a brief review 
of the basic postulates of quantum mechanics, I will derive 
the properties of the quantum mechanical simple harmonic 
oscillator. Then I will consider related models, like the 
charged harmonic oscillator, which brings in the notion of 
charge conservation and antiparticles, and the fermionic 
harmonic oscillator, which introduces the idea of Fermi-Dirac 
statistics and the Pauli exclusion principle. Finally, I 
will generalize to an infinite system of coupled harmonic 
oscillators, which is the basis for the quantum theory of fields.