loading page

Numerical Solution of Schrodinger Equation for Rotating Morse Potential using Matrix Methods with Fourier Sine Basis
  • Aditi sharma,
  • O S K Sastri
Aditi sharma
Central University of Himachal Pradesh
Author Profile
O S K Sastri
Central University of Himachal Pradesh School of Physical and Material Sciences
Author Profile

Abstract

In this paper, an elegant and easy to implement numerical method using matrix mechanics approach is proposed, to solve the time independent Schrodinger equation (TISE) for Morse potential. It is specifically applied to non-homogeneous diatomic molecule HCl to obtain its rotating-vibrator spectrum. While matrix diagonalization technique is utilised for solving TISE, model parameters for Morse potential are optimized using variational Monte-Carlo (VMC) approach by minimizing χ 2 − value. Thus, validation with experimental vibrational frequencies is completely numerical based with no recourse to analytical solutions. The ro-vibrational spectra of HCl molecule obtained using the optimized parameters through VMC have resulted in least χ 2 − value as compared to those determined using best parameters from multiple regression analysis of analytical expressions. Numerical algorithm for solving the Hamiltonian matrix has been implemented utilizing Free Open Source Software (FOSS) Scilab and simulation results are matching well with those obtained using analytical solutions from Nikiforov-Uvarov (NU) method and asymptotic iteration method (AIM).

Peer review status:IN REVISION

09 Jan 2021Submitted to International Journal of Quantum Chemistry
11 Jan 2021Assigned to Editor
11 Jan 2021Submission Checks Completed
14 Jan 2021Reviewer(s) Assigned
14 Jan 2021Review(s) Completed, Editorial Evaluation Pending
14 Jan 2021Editorial Decision: Revise Minor