Separation of variables in (1+2)-dimensional Schrödinger equations

Using our classification of separable Schrödinger equations with two space dimensions published in J. Math. Phys. 36, 5506 (1995) we give an exhaustive description of the coordinate systems providing their separability. Furthermore, we apply these results to separate variables in the heat, Hamilton–Jacobi, and Fokker–Planck equations.