Electron-phonon coupling

A central topic in condensed matter physics is the study of electrons in a periodic potential created by ions in a lattice. The Hamiltonian for a system of ions and electrons can generally be written as –

Here,  Rn and Pn are the positions and momenta of the ions,  and  are the positions and momenta of the electrons,  is the ion-ion potential,  is the electron-ion potential. Note that the electronic and lattice motions are coupled in this Hamiltonian. In general, this is a complex many-body problem even with the simplification afforded by the spatial periodicity of the system.


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