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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
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
FAQ:
- Why do we introduce the ladder operators?
Researcher
The motto in this section is: the higher the level of abstraction, the better.
- Common Question 1
- Common Question 2
Examples
- Example1
- Example2:
History
models/basic_models/harmonic_oscillator.1508686173.txt.gz · Last modified: 2017/12/04 08:01 (external edit)
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