Efficient Energy Level Calculations in InP 2D-Quantum Box with Two Distinct Potentials Using the Sparse Numerov Method

Abstract

In this study, energy level calculations for an InP 2D quantum box structure with two distinct (infinite potential power-exponential) potential potentials have been conducted using the sparse Numerov method. The 2D Schrödinger equation has been transformed in accordance with the sparse Numerov approach, followed by the creation of the solution matrix employing appropriate finite difference expressions. A comparative analysis of calculation results has been performed with respect to CPU time, memory usage, and ground state energy for both O(h^4) and O(h^6) accuracy. The suitability of the sparse Numerov method for 2D nanostructures has been thoroughly discussed. The results revealed that the sparse Numerov approach yields physically meaningful and rational outcomes in the InP 2D quantum box structure. Importantly, it demands significantly lower CPU time and memory resources compared to the classical Numerov method, emphasizing its practical applicability in this context.