Timeline for Why is the harmonic oscillator so important? (pure viewpoint sought). How to motivate its role in Getzler's work on Atiyah-Singer?
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| Jun 30, 2017 at 9:31 | comment | added | Thomas Rot | Back when I did physics it took me a while to realize that this is Hooke's law. Hooke's law states that the motion described by a mass on a spring is given by $m x''=-k x $ for some $k>0$. But this is just saying that from the measurements we see that there is an equilibrium, and that the force is directed opposite from the deviation. Taylor expanding an arbitrary force function with these properties, and cutting the taylor expansion off, which is valid for small deviations, will give you Hooke's law. | |
| Mar 5, 2010 at 2:15 | history | edited | user1504 | CC BY-SA 2.5 |
added 10 characters in body
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| Mar 5, 2010 at 0:02 | comment | added | Theo Johnson-Freyd | More generally, I think the word "harmonic oscillator" essentially means "pure non-zero quadratic function". And these are the first approximation for most systems of interest, or at least for any system where we have any chance of making an approximation. | |
| Mar 4, 2010 at 23:48 | history | answered | user1504 | CC BY-SA 2.5 |