Estimate the band shift with temperature due to electronphonon Frhlich interaction, for an electron band with effective

Estimate the band shift with temperature due to electron–phonon Fröhlich interaction, for an electron band with effective mass equal to the free electron mass, optical phonon energy h̄ω_LO = 30 meV, and ϵ(0)/ϵ₀ = 10 and ϵ(∞)/ϵ₀ = 1. What is the magnitude of the band shift due to the electron–phonon interaction at zero temperature? Even at T = 0, calculation of the electron band energies needs to take into account the vibrations of the lattice.