Quantum Tunneling in Asymmetric Potential Wells: A Computational Approach

Abstract

Quantum tunneling through potential barriers is a cornerstone phenomenon in quantum mechanics with applications in semiconductor devices, nuclear fusion, and quantum computing. This study investigates tunneling in one-dimensional asymmetric potential wells using time-independent and time-dependent computational methods. The asymmetry enhances or suppresses tunneling based on well depth, width, and barrier height. We model various well shapes—such as double-step and trapezoidal potentials—using finite difference and split-operator Fourier techniques. Transmission coefficients, energy eigenvalues, and time-evolution wavefunction dynamics are computed across a parameter space of asymmetry ratios and barrier parameters. Our results demonstrate that slight asymmetries can substantially shift resonant tunneling peaks and alter decay lifetimes. These insights facilitate the design of tunneling-based devices such as asymmetric resonant tunneling diodes and quantum sensors. The computational approach offers adaptability to arbitrary potential profiles and scalability for higher-dimensional systems. Limitations include numerical precision constraints and the exclusion of many-body effects. We propose further extensions that incorporate electron-electron interactions and temperature effects. Overall, this work provides a comprehensive computational framework to explore quantum tunneling in realistic asymmetric geometries.