  We develop a formalism to study the use of Level Set Method (LSM) in the
investigation of evolution of observables in terms of parameters of the
Hamiltonian, both of the system itself and the control part. A simple example
with an analytic solution available perturbatively is examined. We show that B
splines can quite accurately and smoothly interpolate surfaces corresponding to
constant expectation value of observables which form the level sets as
projections on a finite mesh of data. Lastly we make a brief priliminary
scrutiny of teh possibility of using temperature as a relevant parameter in
ensembles of quantum systems.

Quantum Physics