Advanced Quantum Mechanics Schwabl · Problem 4.2

Relativistic Wave Equations and their Derivation

Physics — Quantum Mechanics · classical-damped-harmonic-oscillator-response

Problem

For the classical damped harmonic oscillator

\left(\frac{d^2}{dt^2} + \gamma\frac{d}{dt} + \omega_0^2\right)Q(t) = F(t)/m

determine the following functions:

\chi(\omega)

\chi'(\omega)

\chi''(\omega)

, and

G^>(\omega)

. Hint: Solve the equation of motion in Fourier space and determine the dynamical susceptibility from

\chi(\omega) = \frac{dQ(\omega)}{dF(\omega)}