Commit 4470b0db authored by Gary Steele's avatar Gary Steele
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Update 4_ZPFs.md

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![](figures/4/harmosc.png){style="width:500px"}
Why is the quantum harmonic oscillator such an important concept?
- for small displacements from a minimum, all potentials are approximately harmonic (i.e., parabolic, via Taylor expansion)
- Electrical circuits can be harmonic oscillators
- light and lattice vibrations are descirbed by harmonic oscillators
The last one is particularly interesting, and we can gain a deeper understanding of what "photons" are by looking at how light, and photons, are related to harmonic oscillators.
Imagine an empty box that contains electromagnetic radiation. Classically, each mode of the box is a standing wave that bounces up and down in time:
- mode $1$: $\quad E_1 \cos{(\omega_1 t)} \sin{(\frac{\pi x}{L})}$
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