Abstract
It is as difficult to overestimate the role of harmonic oscillator models in physics in general and in quantum mechanics in particular as the influence of Beatles and Led Zeppelin on modern popular music. Harmonic oscillators are ubiquitous and appear every time when one is dealing with a system that has a state of equilibrium in the vicinity of which it can oscillate, i.e., in a vast majority of physical systems—atoms, molecules, solids, electromagnetic field, etc. It also does not hurt their popularity that the harmonic oscillator is one of the very few models which can be solved exactly.
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- 1.
The irony is that an explanation of photoelectric effect did not require the quantization of light despite what you might have read or heard. All experimental data could have been explained treating light classically while describing electrons in metals by the Schrödinger equation. Fortunately Einstein did not have the Schrödinger equation in 1905 and couldn’t know that. The science does evolve in mysterious ways: Einstein’s erroneous idea about the photoelectric effect inspired de Broglie and Schrödinger and brought about the Schrödinger equation, which could have been used to disprove the idea. Compton’s effect, on the other hand, can indeed be considered as a proof of reality of photons.
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P.A.M. Dirac, The quantum theory of the emission and absorption of radiation. Proc. R. Soc. Lond. 114, 243 (1927).
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It is interesting that the term “photon” was used for the first time in an obscure paper by an American chemist Gilbert Lewis in 1926. His paper is forgotten, but the term he coined lives on.
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Deych, L.I. (2018). Harmonic Oscillator Models. In: Advanced Undergraduate Quantum Mechanics. Springer, Cham. https://doi.org/10.1007/978-3-319-71550-6_7
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DOI: https://doi.org/10.1007/978-3-319-71550-6_7
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