A general formalism of the problem of perfect state transfer is presented.
We show that there are infinitely many Hamiltonians which may provide solution to
this problem. In a first attempt to give a classification of them we investigate
their possible forms and the related dynamics during the transfer. Finally, we show how the present formalism can be used for the engineering of perfect quantum wires of various topologies and coupling configurations. This is a common work with G.M. Nikolopoulos and I. Jex.