Reduced role of the wavefunctions' curvature of quantum potentials in non-standard quantum systems

Abstract

In standard quantum systems where the mass of the particles is a constant, the quantum potential is exclusively dictated by the curvature of the wavefunction. Quantum systems with spatially dependent (effective) mass distributions appear in different systems, such as an electron in a semiconductor, quantum dots, and quantum liquids. In this letter, we show a class of quantum systems where the effective mass distribution governs the quantum potential rather than the wavefunctions' curvature for the entire region occupied by the wavefunction or at least for a sub-region in space. This gives a new insight into the role of the wavefunction's curvature in non-standard quantum systems, followed by the quantum potential in which quantum effects emerged in the Madelung reformulation of the Schrödinger equation.