Solving exact solution of time independent Schrodinger wave equation and visualizing eigenfunctions using XCOS

Abstract

Time independent Schrodinger wave equation (SWE) for a quantum system can be solved computationally which involves application of numerical method. Different computational tools used to solve SWE involving different potentials were reviewed. XCOS, an inbuilt tool of Scilab for modelling and simulating hybrid dynamic system and is an open-source is used to solve the Schrodinger wave equation for different quantum systems. Only basic understanding of mathematics up to high school level is required to solve Schrodinger wave equation using XCOS. Different quantum systems considered are free particle in a well bounded by infinite potential at the boundaries, radial part of SWE for Hydrogen atom under coulombic potential, screened coulombic potential. Radial part of Schrodinger wave equation for a particle under harmonic and anharmonic potential were also solved using XCOS computational tool. Eigenvalues and eigenvectors were obtained by solving radial part of Schrodinger wave equation for molecules under Morse potential. Advantages and limitation of XCOS computational tools were also discussed. We argue in favour of the academic use of computational tool XCOS to solve Schrodinger wave equation in introductory quantum mechanics courses.