In the present paper, we see the manner of the propagation of the wave packet in the presence of a scatterer and we see the form of the scattered packet. The form of the scattered packet at the detector is closely related to the form of the energy spectra. The general form of the energy spectra is given in connection with the wave packet nature of the scattered beam. Of course, this energy spectra tends to the conventional Lorentzian type in the stationary limit. In Part I of the present paper, the relation between the form of the scattered packet and the cross section is discussed in detail.