Position-dependent effective masses in semiconductor theory

A Hamiltonian possessing a position-dependent effective mass is sometimes employed to describe the motion of free carriers (electrons and holes) in semiconductors of nonuniform chemical composition. In the present investigation it is shown that Hamiltonians representative of carriers possessing position-dependent masses are not Galilean invariant, and that approximation schemes which lead to position-dependent mass equations are not unique. The concept of a position-dependent mass should, therefore, be abandoned. von Roos (1982) has shown how to circumvent the difficulties associated with position-dependent masses.