Fisher information and quantum systems with position-dependent effective mass

We show that effective masses in nonrelativistic quantum mechanics arise in a natural fashion from the Frieden and Soffer's Principle of Extremal Information (EPI) when the mean values of operators involving the momentum p̂ and exhibiting the form p̂f(x̂)p̂ are included as constraints. A position-dependent effective mass, which is currently used in the literature as a simple model for diverse phenomena in quantum physics, appears after extremalizing Fisher's information measure with the above constraints.