Quantum tunneling from a new type of generalized Smith-Volterra-Cantor potential

In this paper, we introduce and analyze the Smith-Volterra-Cantor potential of power $n$, denoted as SVC$(\rho ,n)$. Bridging the gap between the general Cantor and SVC systems, this novel potential offers a fresh perspective on Cantor-like potential systems within quantum mechanics that unify fractal and non-fractal potentials. Utilizing the Super Periodic Potential (SPP) formalism, we derive the close form expression of the transmission probability $T_G(k)$. Notably, the system exhibits exceptionally sharp transmission resonances, a characteristic that distinguishes it from other quantum systems. Furthermore, the multifaceted transmission attributes of the SVC$(\rho ,n)$ are found to be critically dependent on both parameters, $\rho$ and $n$, offering an intricate interplay that warrants deeper exploration. Our findings highlight a pronounced scaling behavior of reflection probability with $k$, which is underpinned by analytical derivations.