Electrons oscillate in response to the applied EM fields, and their motion is damped by the...

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Electrons oscillate in response to the applied EM fields, and their motion is damped by the collision and can be expressed as, d2 * т dt2 + y dt suppose that the electron density displacement and the electric field are in phase such that the displacement x (t) is given as i (t) = xỏ e-iwt and electric field as E (t) = E, e-iwt. Show that a. ) the displacement vector e E (t) m ( w2 + iyw) * (w,t) %3D b. ) the polarization vector - ne? È (t) β (ω) - m (w2 + iy w) c. ) the dielectric function 2 пе2 Wp ω2+ ίγω E (w) = 1- m E, Electrons oscillate in response to the applied EM fields, and their motion is damped by the collision and can be expressed as, d2 * т dt2 + y dt suppose that the electron density displacement and the electric field are in phase such that the displacement x (t) is given as i (t) = xỏ e-iwt and electric field as E (t) = E, e-iwt. Show that a. ) the displacement vector e E (t) m ( w2 + iyw) * (w,t) %3D b. ) the polarization vector - ne? È (t) β (ω) - m (w2 + iy w) c. ) the dielectric function 2 пе2 Wp ω2+ ίγω E (w) = 1- m E,