What actually happens when a photon strikes an atom?

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I know that when a photon strikes an atom, it excites an electron, which then will re-emit the photon when it returns to normal. But what is actually happening here? Is it really as simple as that, or is there something more fundamental going on here, like how nuclei are bound together using carrier particles?
 
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Low-energy photons interact with the atomic electrons and their energy levels, basically like you described. This usually means visible or near-visible (infrared or ultraviolet). With heavier atoms you can also get this sort of interaction using X-ray photons. The nucleus basically doesn't come into play except in the sense that its attraction of the electrons (inserted into Schrödinger's equation) creates the discrete energy levels. Differences in shape or spin of the nucleus can cause very small effects on the electron energy levels. Look up "fine structure" and "hyperfine structure" in atomic spectra.

High-energy photons such as in gamma rays can interact directly with the nucleus, in which case the electrons are not involved.
 
Not an expert in QM. AFAIK, Schrödinger's equation is quite different from the classical wave equation. The former is an equation for the dynamics of the state of a (quantum?) system, the latter is an equation for the dynamics of a (classical) degree of freedom. As a matter of fact, Schrödinger's equation is first order in time derivatives, while the classical wave equation is second order. But, AFAIK, Schrödinger's equation is a wave equation; only its interpretation makes it non-classical...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. Towards the end of the first lecture for the Qiskit Global Summer School 2025, Foundations of Quantum Mechanics, Olivia Lanes (Global Lead, Content and Education IBM) stated... Source: https://www.physicsforums.com/insights/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect/ by @RUTA
Is it possible, and fruitful, to use certain conceptual and technical tools from effective field theory (coarse-graining/integrating-out, power-counting, matching, RG) to think about the relationship between the fundamental (quantum) and the emergent (classical), both to account for the quasi-autonomy of the classical level and to quantify residual quantum corrections? By “emergent,” I mean the following: after integrating out fast/irrelevant quantum degrees of freedom (high-energy modes...

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