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I'm working through the scattering sections of Mechanics by Landau and Lifshitz, and wanted to know if/how physicists today employ the methods of purely classical scattering processes. As far as I can surmise, these are useful for

  1. Understanding Rutherford Scattering in the gold foil experiment and
  2. Introducing concepts like the scattering cross-section for its application in quantum mechanics.

In Goldstein's Classical Mechanics, the author argues that since conservation of momentum and energy apply generally, one can often view scattering processes as a "black box" wherein it doesn't matter if the process is classical or quantum. But Landau/Lifshitz say that actually calulating the angles of deflection/cross-sections requires knowledge of the form of the interaction. Furthermore, if you observe diffractive scattering of particles, isn't the whole experiment necessarily quantum in nature and hence requires the full quantum mechanical treatment?

So my question is:
What are some examples of modern applications of classical scattering theory, and what are the justifications for why the quantum methods were not necessary? How do physicists today employ classical scattering theory?

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    $\begingroup$ "What are some examples of modern applications of classical scattering theory," Ask the guys interested in the structure and collisions of galaxies and globular clusters. $\endgroup$ Aug 8, 2016 at 21:48

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High quality models for CAT (computer-aided tomography) use classical scattering to describe the propagation of radiation inside a body. Similarly, classical scattering is used in practically all methods for nondestructive testing.

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Here is a quote from Eric Heller: "Random waves are the paradigm for quantum chaos. This is as close as quantum mechanics can come to chaos." Depending on the physical system you will see Anderson Localization, Quantum ergodicity and many more phenomena, with classical waves. Anderson Localization can be seen to arise from the cumulative effect of multiple scattering. I don't know of a classical analog for entanglement, but many of the studies of quantum chaos use classical analog systems. Another great example is the transition from Poissonian to Wigner statistics in classical systems which are perturbed away from separability. Level repulsion is another example.

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