Numerical solution of Schrodinger equation for rotating Morse potential using matrix methods with Fourier sine basis and optimization using variational Monte‐Carlo approach

In this paper, time independent Schrodinger equation (TISE) for rotating Morse potential is solved numerically using matrix mechanics approach with Fourier sine basis, to obtain the ro-vibrational spectra for diatomic molecules, here for HCl. Alongside, an optimization procedure for extraction of best model parameters based on variational Monte-Carlo technique (VMC) is implemented. The first three vibrational frequencies from simulation are compared with experimental data by calculating mean-square error, called chi(2)-value. Minimizing chi(2) by VMC technique is akin to extracting inverted potential based on Morse function that best fits experimental data. Finally, these optimized parameters for Morse potential, along with centrifugal term, are utilized in TISE to obtain ro-vibrational frequencies for HCl. It has been found that mean % error obtained for ro-vibrational lines from VMC are two orders of magnitude smaller than those obtained from best parameter fits using multiple regression analysis. The programs have been implemented in Scilab, and matrix methods results have been validated with those obtained using analytical solutions from Nikiforov-Uvarov method and asymptotic iteration method.