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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 .
Both
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
second kind.

The discrete time evolution is obtained by iterating the map

on .
The unitary nature of the evolution is also evident because

on are conjugated by using

*Oliver Knill *

Tue Aug 18, 1998