Mapping of two-dimensional Schrödinger equation under the point transformation

For the two-dimensional Schrodinger equation, the general form of the point transformations such that the result can be interpreted as a Schrodinger equation with effective (i.e., position dependent) mass is studied. A wide class of such models with different forms of mass function is obtained in this way. Starting from the solvable two-dimensional model, the variety of solvable partner models with effective mass can be built. Several illustrating examples not amenable to conventional separation of variables are given.