Fisher information and quantum systems with position-dependent effective mass

Abstract

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 p and exhibiting the form p f(x) p 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.