Linear systems have the feature that the solutions obey the Principle of Superposition, that is, the amplitudes add linearly for the superposition of different oscillatory modes. The standard deviatio...Linear systems have the feature that the solutions obey the Principle of Superposition, that is, the amplitudes add linearly for the superposition of different oscillatory modes. The standard deviation \(\sigma (t) = \sqrt{\langle t^2 \rangle − \langle t \rangle^2}\) characterizing the width of the amplitude of the wavepacket spectral distribution in the angular frequency domain, \(\sigma_A(\omega )\), and the corresponding width in time \(\sigma_A(t)\), are related by :
