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How does the wave-particle duality exhibited by electrons and the wave-like nature of phonons enable their interaction in solid-state systems?

Can you explain the underlying mechanisms that allow for energy and momentum exchange between phonons and electrons, particularly in the context of electron-phonon scattering and the modulation of electronic properties by lattice vibrations?

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  • $\begingroup$ I'm not sure I understand the question. The wave-particle duality applies also to phonons. In any case, whether something is a particle or a wave is not particularly relevant when setting up a scattering problem. Generally, one writes down a Hamiltonian directly, and calculates matrix elements. In my opinion, J. M. Ziman's book "Electrons and Phonons", Oxford (1960) is still among the clearest and most detailed treatments of the formalism in this context. $\endgroup$
    – Anyon
    Nov 26, 2023 at 18:11
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    $\begingroup$ I might be lacking the full understanding of how to treat phonons but from what I have read, phonons are quasiparticles. Can we tread quasiparticles the same way as fundemental particles in terms of wave-particle duality? and for the phonon-electron interaction, such interaction would include momentum exchange, and as I know this is a property of particles not waves. Moreover, thanks for the reference. $\endgroup$ Nov 27, 2023 at 0:09
  • $\begingroup$ Yes, they are quasiparticles or collective excitations, but this doesn't stop them from displaying decidedly particle-like properties under the right circumstances. In particular, the theory of phonons allows for a single phonon to be emitted by a single atom, travel through the material as a wave, and then be absorbed as a single phonon. I'd argue their delocalized nature in-between such events is naturally understood in terms of crystal momentum. Intuitively, wavelength and crystal momentum are related through de Broglie's relation. $\endgroup$
    – Anyon
    Nov 27, 2023 at 14:48
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    $\begingroup$ In general, I would recommend never treating anything as a particle in quantum mechanics, just think of "particles" as having localised wavefunctions. $\endgroup$ Dec 2, 2023 at 2:57
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    $\begingroup$ @NikeDattani I got your point, thank you again for the clarification. $\endgroup$ Dec 20, 2023 at 1:51

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