Closed-form symbolic evaluation of the Lorentz dielectric function at resonance. Substituting ω = ω₀ kills the ω₀² − ω² numerator in the denominator of ω_p²/(ω₀²−ω²−iγω), leaving ε(ω₀) = 1 + ω_p²/(−i·γ·ω₀) = 1 + i·ω_p²/(γ·ω₀). Real part:…
Closed-form symbolic evaluation of the Lorentz dielectric function at resonance. Substituting ω = ω₀ kills the ω₀² − ω² numerator in the denominator of ω_p²/(ω₀²−ω²−iγω), leaving ε(ω₀) = 1 + ω_p²/(−i·γ·ω₀) = 1 + i·ω_p²/(γ·ω₀). Real part:…