Calculation of the Lindhard Response Function Using the formula of first-order stationary perturbation theory, ψk=ψk^0 ∑k^' (1)/(εk-εk)(ψ𝐤^0, V ψ𝐤^0) ψk^0 and expressing the charge density as ρ(𝐫)=-e ∑fk ψk(r)^2=ρ^0(r) ρ^i n d(r) (where f2 is the equilibrium Fermi distribution), show that the Fourier transform of the charge (Equation (17.56) then follows from the definition (17.37) of χ (q).) | Numerade
Calculation of the Lindhard Response Function Using the for…
Jul 21, 2021
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Calculate the Lindhard functions (as defined in Eq. (15.93)) in 1D and 2D, and show that the singularity at q=2 kF is stronger than that of the 3D case in Eq. (15.94) in both cases. In particular, the logarithmic divergence in 1D is closely related to the (logarithmic) Peierls instability we encountered in Chapter 7. | Numerade
Calculate the Lindhard functions (as defined in Eq. (15.93)) in 1D and 2…
Jun 19, 2023
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