  The problem considered here is the determination of the hamiltonian of a
first quantized nonrelativistic particle by the help of some measurements of
the location with a finite resolution. The resulting hamiltonian depends on the
resolution of the measuring device. This dependence is reproduced by the help
of a blocking transformation on the wave function. The systems with quadratic
hamiltonian are studied in details. The representation of the renormalization
group in the space of observables is identified.
