Large amplitude vibrational motion in a one dimensional chain: Coherent state representation

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Abstract
A study is made of the quantum mechanical motion of a one dimensional finite chain of anharmonic oscillators with free ends. It is shown that, for states which time evolve as coherent states (minimum uncertainty wave packets) of the normal mode vibrations, the motion is equivalent to a classical system with an effective potential interaction determined by convoluting the quantum wave packet and the potential energy. Some examples are discussed, with particular attention given to the Toda and Morse potentials, which are shown to be invariant in form under this convolution. The similarities between the classical Toda and Morse lattices are then utilized to infer the existence of compressional solitary waves in the Morse lattice from the well known soliton solutions of the Toda lattice. Further, for the Morse lattice an analytic expression is found for the first order perturbative correction to the Toda solitons for large amplitude vibrations. We also discuss the relation between the existence of such solitary waves and the rate of vibrational relaxation in molecular systems.