Wave function for smooth potential and mass step

The one-dimensional Schrodinger equation, derived from the general form of the effective-mass Hamiltonian (m(eta)pm(epsilon)pm(rho)+ m(rho)pm(epsilon)pm(eta))/4 +V with eta + epsilon +rho = - 1, is solved exactly for a system with smooth potential and mass step. The wave function depends on the Heun function, which is a generalization of the hypergeometric function. The effective-mass Hamiltonian and the connection rules for a system with abrupt heterojunction are deduced from the study of the limiting case when the smooth step potential and mass tend to an abrupt potential and mass step. [1050-2947(99)05101-X].