Absorption by an Oscillator

EgJd) being zero outside the. interval t 0 to t — T as is real, the conjugate complex quantity satisfu -s the equation 

Analogous relationships liold for thci two otlu. r components. According to the laws of olectro(lynainie.s, the total energy-density of the radiation field is then given by 

Hence for the total density of radiation we obtain the expression 

After these preliminary remarks on the radiation field we now pass on to the equation giving the vibrations of the linear harmonic oscillator. If the oscillator is capable of vibrating only in the r-direction, this equation is 

as we know, the most general solution of a non-homogeneous differential equation is obtained by adding one solution of the non-homogeneous equation to the general solution of the homogeneous equation. This last may be written in the form 

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