|
, 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
