Abstract
In this paper, we introduce and analyze the Smith-Volterra-Cantor potential of power n , denoted as SVC(ρ, 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(ρ, n) are found to be critically dependent on both parameters, ρ 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.