Energy Levels and Absorption Coefficients for Diverse Bounded Potentials: A Comprehensive Analysis

This article presents a comprehensive numerical investigation into the energy levels and absorption coefficients within quantum well structures, with a particular focus on the GaAs/AlGaAs system. Various bounded potentials, including the Rosen-Morse potential, Wood-Saxon potential, Pöschl-Teller potential, Razavy potential, inversely quadratic Hellmann potential, Kratzer-Fues potential, and Morse potential, are explored. Employing the Schrödinger equation, with considerations for effective mass and envelope function approximations, a discrete formulation is attained through finite differences. Throughout the analysis, the effective mass ratio is upheld as a constant value characteristic of GaAs. The study reveals that transition energies and absorption coefficients exhibit subtle variations in response to alterations in well parameters, spanning from the lower bounds of the near-infrared spectrum to the midpoints of the far-infrared region. By comprehensively studying these phenomena across a spectrum of potentials, this research contributes valuable insights into the behavior and characteristics of quantum well structures, particularly within the context of the GaAs/AlGaAs system.