Quantum Tunneling With Linear Potential: Case Studies in Biological Processes

Quantum biology, at the intersection of quantum mechanics and biology, investigates the involvement of quantum phenomena in biological processes. A pivotal focus is quantum tunneling, wherein particles traverse energy barriers, a phenomenon with potential significance in various biological contexts. This article introduces a new class of linear potential functions for studying quantum tunneling in biological processes. The simplicity of linear potentials enables analytical solutions to the Schrödinger equation, offering efficiency compared to more complex numerical methods. The proposed linear potential functions are derived using parabolic curves, providing an analytical form with physical interpretations. The corresponding energy function and transmission coefficients are presented, facilitating a simplified understanding of tunneling behavior. Theoretical implications of the proposed model are discussed, emphasizing the ease of parameter variation and its applicability to diverse biological scenarios. In the numerical demonstration, two case studies are presented: (1) examining proton tunneling in DNA point mutations and (2) exploring electron tunneling in biological receptors, specifically the ACE2 receptor in the context of SARS-CoV-2.