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

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 G C and Smith-Volterra-Cantor S V C 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 formalism, we derive the close form expression of the transmission probability T<inf>G</inf>(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. © 2025 Author(s).