  Several standard processes for searching minima of potential functions, such
as thermodynamical strategies (simulated annealing) and biologically motivated
selfreproduction strategies, are reduced to Schr\"odinger problems. The
properties of the landscape are encoded in the spectrum of the Hamiltonian. We
investigate this relation between landscape and spectrum by means of
topological methods which lead to a possible classification of landscapes in
the framework of the operator theory. The influence of the dimension $d$ of the
search space is discussed. The connection between thermodynamical strategies
and biologically motivated selfreproduction strategies is analyzed and
interpreted in the above context. Mixing of both strategies is introduced as a
new powerful tool of optimization.
