Abstract
We introduce a marginal picture of the evolution of quantum systems, in which the representation vectors are the quantities that evolve and operators and wave packets remain static. The representation vectors can be seen as probe functions that are the evolution of a $\ensuremath{\delta}$ function with initial support on $q=X$ in coordinate space. This picture of the dynamics is suited for the determination of intrinsic arrival distributions for quantum systems, providing a clear physical meaning to the ``time eigenstates'' used in these calculations. We also analyze Galapon et al.'s ``confined time eigenstates'' [Phys. Rev. Lett. 93, 180406 (2004)] from this point of view, and propose alternative probe functions for confined systems without the need of a quantized time.
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