  We propose a dynamical system of tumor cells proliferation based on
operatorial methods. The approach we propose is quantum-like: we use ladder and
number operators to describe healthy and tumor cells birth and death, and the
evolution is ruled by a non-hermitian Hamiltonian which includes, in a non
reversible way, the basic biological mechanisms we consider for the system. We
show that this approach is rather efficient in describing some processes of the
cells. We further add some medical treatment, described by adding a suitable
term in the Hamiltonian, which controls and limits the growth of tumor cells,
and we propose an optimal approach to stop, and reverse, this growth.
