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.
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
 to incorporate the modified Morse potential
function , 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.