  The dynamics of a quantum mechanical particle in a time-independent potential
are found to contain many interesting phenomena. These are direct consequences
of the (typical) existence of more than one time scale governing the problem.
This gives rise to full revivals of initial wavepackets, fractional revivals
(multiple wavepackets appearing at fractions of the revival time) and the
striking quantum carpets. A variety of analytic techniques are used to consider
the interference that gives rise to these phenomena while skirting calculations
involving cross-terms. Novel results include a new theorem on the weighting
coefficients $a_m$ that govern fractional revivals, a demonstration that
$\Psi_{cl}$, the function that governs the distribution and features of these
fractional revivals, really does behave classically, a treatment of the
wavepacket dephasing in the infinite square well by means of the Poisson
summation formula, and a correct analysis of the spatial distribution of
intermode traces. Also, this work presents a coherent treatment of these
phenomena, which before now did not exist.
