Calculating resonance position and lifetime using modified smooth exterior scaling for piecewise one-dimensional potentials

Abstract

Abstract The primary objective of this paper is the systematic investigation of the applicability and numerical behaviour of the modified smooth exterior scaling (MSES) framework for piecewise and non-trivial one-dimensional problems. Studying these piecewise potentials is important for analysing resonance states in heterostructures, semiconductor devices, double-barrier diodes and understanding low-dimensional structures like quantum well devices. The non-analytic nature of the potentials studied makes complex scaling ineffective; therefore, smooth exterior scaling (SES) is required. To provide improved outgoing boundary conditions compared to the SES method, MSES has proven to be an efficient technique that eliminates artificial reflections. This methodology can also be applied in cases where analytical solutions are unattainable. In this paper, the metastable states corresponding to different piecewise potentials are calculated using the MSES method. The wave functions corresponding to these metastable states are computed and plotted for various resonance energies.