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Has anybody attempted a pedagogical introduction to the interaction between an atom and the electromagnetic field using this one-dimensional system? Both the atom and the quantum field are represented by spring(s) and mass(es), and weak coupling is achieved by a spring with small spring constant, k. This spring exerts a small attractive force by Hooke's law, F=-k(Xatom-Xmass), between the atom and the central black mass that represents the field at one point. The system can be solved by finding the normal modes of the classical Hamiltonian and reducing it to a system of independent SHOs. Many years ago, I did something like this for the Mossbauer Effect, where I showed how the gamma ray can deliver its momentum to a phonon.

Qmechanic
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Guy Vandegrift
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1 Answers1

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Second page in, on Zee's QFT in a Nutshell, he has:

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He then starts to construct a colossal Langrangian (but not suprisingly gives up quickly) based around the p.e. and k.e. of every point in the "mattress" . He also bemoans the fact that "we have not been able to get away from this idea of harmonic oscillators and wavepackets" as the bedrock of theoretical physics for 75 plus years.