  We introduce a new type of potential system that combines the families of
general Cantor (fractal system) and general Smith-Volterra-Cantor (non-fractal
system) potentials. We call this system as Unified Cantor Potential (UCP)
system. The UCP system of total span $L$ is characterized by scaling parameter
$\rho >1$, stage $G$ and two real numbers $\alpha$ and $\beta$. For $\alpha=1$,
$\beta=0$, the UCP system represents general Cantor potential while for
$\alpha=0$, $\beta=1$, this system represent general Smith-Volterra-Cantor
(SVC) potential. We provide close-form expression of transmission probability
from UCP system for arbitrary $\alpha$ and $\beta$ by using $q$-Pochhammer
symbol. Several new features of scattering are reported for this system. The
transmission probability $T_{G}(k)$ shows a scaling behavior with $k$ which is
derived analytically for this potential. The proposed system also opens up the
possibility for further generalization of new potential systems that encompass
a large class of fractal and non-fractal systems. The analytical formulation of
tunneling from this system would help to study the transmission feature at
breaking threshold when a system transit from fractal to non-fractal domain.
