Abstract
Recently, Plyukhin and Schofield have shown that there is a close analogy between collective oscillation of a system composed of an assembly of interacting particles and the propagation of a free quantum particle in one dimension. They could not have interpreted some of the equations involved in this analogy. We show here that the arbitrary field, they have introduced, satisfies the Klein-Gordon equation, too. Moreover, the arbitrary field is proportional to the local electric field. This local electric filed may induce a transition between the two-particle states; one moving to the left and the other to the right with the speed of light.