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models:basic_models:harmonic_oscillator
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Harmonic Oscillator: $\quad L= \frac{m}{2} \left(\frac{dx}{dt}\right) - \frac{k}{2}x^2$
Intuitive
Concrete
- A good description can be found at http://www.hep.caltech.edu/~fcp/physics/quantumMechanics/SHO/SHO.pdf
Abstract
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
FAQ
- Why do we introduce the ladder operators to treat the harmonic oscillator in quantum mechanics?
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models/basic_models/harmonic_oscillator.1522220795.txt.gz · Last modified: 2018/03/28 07:06 (external edit)
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