A program is available for these calculations free of charge with the corresponding author, with applications on the six potential energy curves:

Morse potential, Lenard Jones potential, RKR potential, ab initio potential, Simon-Parr-Finlin (Kratzer) potential, and Dunhum potential.

Morse potential is assumed to describe the single-pair atomic interaction included in the derived anharmonic interatomic effective potential.

When

Morse potential [[omega].sup.(1)](r) = -([gamma]/2)[e.sup.-r] - m - [lambda]/2 + 1/2 - k/r and 3-dimensional oscillator potential [[omega].sup.(2)](r) = ([gamma]/4)r - ([lambda] + m - 1/2)(2/r) - k/r are considered as the gauge field potentials, the upper spinor components are associated with generalized Laguerre polynomials.

The

Morse potential has many unique analytic properties, which makes it especially suitable for modelling.

To avoid the influence of equivalent potential functions, the two-body

Morse potential is adopted to simulate the interaction between the carbon atoms in diamond indenter and silicon atoms in the specimen.

where [r.sub.ij] is the distance between the ith and jth atoms, and [r.sub.e,ij], [D.sub.e,ij], and [B.sub.ij] are parameters associated with a

Morse potential for the isolated i-j diatom, which are adjusted by experimental data.

One aim of our work is the calculation of matrix elements for the

Morse potential:

[16] to incorporate the modified

Morse potential function [17], to estimate elastic constants and stress-strain relationships of nanotubes under tensile and torsion loadings.

In this section, we demonstrate the viability of the canonical algebra as discussed in Section 2 for obtaining energy eigenvalue and eigenfunctions for q-deformed

Morse potential. The time-independent Schrodinger equation is given by

We also have in mind that the inter-site

Morse potential favours the excitation of soliton-like modes.

Han, "Any l-state solutions of the

Morse potential through the Pekeris approximation and Nikiforov-Uvarov method," Chemical Physics Letters, vol.

Berkdemir, "Pseudospin symmetry in the relativistic

Morse potential including the spin-orbit coupling term," Nuclear Physics A, vol.