One of the important challenges facing theorists is the com-
putation of real time quantum dynamics in systems with "many" degrees
of freedom. The need arises for diverse problems, ranging from quantum
computation, quantum control, to spectroscopy, condensed phase chemis-
try and physics and more. In this talk I will present a brief overview
of the need for quantum dynamics computations; of the different appro-
aches being tested and applied by various groups and recent progress
made in my group in developing methods for computing real and imagin-
ary time quantum dynamics.
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