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\begin{document}

\title{Numerical Solution of Schrodinger Equation for Rotating Morse Potential
using Matrix Methods with Fourier Sine Basis}



\author[1]{Aditi sharma}%
\author[2]{O S K Sastri}%
\affil[1]{Central University of Himachal Pradesh}%
\affil[2]{Central University of Himachal Pradesh School of Physical and Material Sciences}%


\vspace{-1em}



  
  \date{May 26, 2024}


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\begin{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 \selectlanguage{greek}χ \selectlanguage{english}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 \selectlanguage{greek}χ \selectlanguage{english}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).%
\end{abstract}%



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