The Schrödinger with variable mass model: mathematical analysis and semi-classical limit
In this paper, we propose and analyze a one-dimensional stationary quantum-transport model: the Schrodinger with variable mass. In the first part, we prove the existence of a solution for this model, with a self-consistent potential determined by the Poisson problem, whereas, in the second part, we rigorously study its semi-classical limit which gives us the kinetic model limit. The rigorous limit was based on the analysis of the support of the Wigner transform.