Abstract
A relevant relation between the dwell time and the density of states for a three-dimensional system of arbitrary shape with an arbitrary number of incoming channels is derived. This result extends the one obtained by Gasparian and co-workers for the case of a one-dimensional symmetrical potential barrier. We believe that such a strong relation is rich in physical significance because the dwell time is the most widely accepted time measure of a particle’s dynamics and the density of states in a given region is one of the most relevant properties of a system in equilibrium.
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