Potential energy inherited by a system plays a significant role in the system analysis. The potential energy operators are not generalized till date. Each system has its unique basis to explain the same. This article provides a novel approach to determine a generalized potential operator for a particle using Poisson's equation in a set basis in accordance with the corresponding characteristics manifested by the unit elements of basis. The mathematics includes the fundamental definitions of quantum physics and geometrical inference of manifolds. We shall see that the operator itself is time variant and medium dependent, which in turn depicts the evolution of the system in different mediums.

operator, potential operator, Poisson’s equation, manifolds, manifold arrangement, current conservation law, time evolution