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We consider the large polaron described by the Fr\"ohlich Hamiltonian andstudy its energy-momentum relation defined as the lowest possible energy as afunction of the total momentum. Using a suitable family of trial states, wederive an optimal parabolic upper bound for the energy-momentum relation in thelimit of strong coupling. The upper bound consists of a momentum independentterm that agrees with the predicted two-term expansion for the ground stateenergy of the strongly coupled polaron at rest, and a term that is quadratic inthe momentum with coefficient given by the inverse of twice the classicaleffective mass introduced by Landau and Pekar.

Optimal parabolic upper bound for the energy-momentum relation of a strongly coupled polaron