Essentially the difference is that free electrons, as the name implies, do not experience a restoring force, unlike a spring when it is either stretched or compressed. Therefore, if you remove the eigenfrequency from the Lorentz-Drude model you end up with the Drude model that allows to model the dielectric function of metals (certainly, metals also have electronic transitions in addition, otherwise gold and copper would not be colored). The plasma frequency is the frequency above which the real part of the dielectric function becomes positive and the metal starts to behave like a dielectric.

The Lorentz-Drude model for estimation of the plasma frequency is applicable only for semiconductor with non-degenerate electron gas, and it is not applicable for metals, because in conductivity of metals according to the Pauli principle and Fermi-Dirac statistics takes part only free randomly moving electrons with energy ear the Fermi level energy.

Dear Aijaz Ali

I agree with Prof. Vilius Palenskis

For instance, you can see for example that in Feynman Lectures on Physics, the useful Lorentz-Drude model is not explained.

I suggest you to follow :https://eng.libretexts.org/Bookshelves/Materials_Science/Supplemental_Modules_(Materials_Science)/Semiconductors/Plasmon_Resonance

https://www.sciencedirect.com/topics/physics-and-astronomy/plasma-frequencies

https://www.researchgate.net/post/How_do_I_calculate_the_resonance_and_plasma_frequency_of_bulk_metals

Thomas Mayerhöfer I can understand that plasma frequency is actually a resonant frequency in Drude Model As w_0 =0 in Drude model, but what I am not able to understand is what is plasma frequency in Lorentz model where w_0 is not equal to zero. If plasma frequency is the resonant frequency in Lorentz model then what is w_0 ? OR

Is plasma frequency any frequency(e.g applied field frequency) with which the plasma is oscillating in Lorentz model?

Thanks

Naeem Khan Actually, the plasma frequency is the oscillator strength of the plasmon (and, also, in the Lorentz-model). If you want more details, have a look at my lecture notes under Preprint Wave optics in Infrared Spectroscopy