Higher‐order special self‐adjoint equations and particle dynamics

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Abstract
We exhibit a remarkable connection between a hierarchy of higher‐order special self‐adjoint ordinary differential equations and the description of motion of a cluster of particles in classical mechanics. The cluster is assumed to consist of equal mass particles all moving in one dimension. In a perturbation schema based on the first‐order equation of motion of the center of mass point, the time evolution of the moments of order m−1 is governed by the solution of a special self‐adjoint equation of order m. A similar connection exists for the moments of a wave packet in quantum mechanics.