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Fr\"{o}hlich's polaron Hamiltonian describes an electron coupled to thequantized phonon field of an ionic crystal. We show that in the strong couplinglimit the dynamics of the polaron is approximated by an effective non-linearpartial differential equation due to Landau and Pekar, in which the phononfield is treated as a classical field.

Derivation of an effective evolution equation for a strongly coupled polaron