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Let L be a bounded selfadjoint operator on a separable Hilbert space H.
After a rescaling , which corresponds to
a change of time in the evolution, we can assume that .
Assume solves . The unitary operators
are independent of the choice of .
solve and has its spectrum in .
Here is the n'th
Chebychev polynomial of the first kind and
is the n'th Chebychev function of the
The discrete time evolution is obtained by iterating the map
The unitary nature of the evolution is also evident because
on are conjugated by using
Tue Aug 18, 1998