Thesis Summary:

In order to treat open quantum systems involving Hamiltonians with singular potential, we develop the variational formulation of the linear and non-linear Schrödinger stochastic equations with infinite-dimensional state spaces. In particular, we establish the existence and uniqueness of regular solutions of these stochastic evolution equations. In addition, we prove that the mean value of the square of the norm of the variational solution of the linear equation of stochastic Schrödinger is constant.