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models:basic_models:harmonic_oscillator
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Harmonic Oscillator
Why is it interesting?
“The career of a young theoretical physicist consists of treating the harmonic oscillator in ever-increasing levels of abstraction.” Sidney Coleman
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. Gregory L. Naber
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.
The Simple Harmonic Oscillator by F. Porter
Layman
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.
Student
- A good description can be found at http://www.hep.caltech.edu/~fcp/physics/quantumMechanics/SHO/SHO.pdf
Researcher
Examples
- Example1
- Example2:
FAQ
- Why do we introduce the ladder operators?
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History
models/basic_models/harmonic_oscillator.1511426266.txt.gz · Last modified: 2017/12/04 08:01 (external edit)
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