Morse potential energy spectra through the variational method and supersymmetry

The rotating Morse potential model for diatomic molecules in the tridiagonalJ-matrix representation: I. Bound states

“…Then, for a selected value of λ from within the plateau, we compute the eigenvalues of the full Hamiltonian and compare them with available numerical results for the given molecule. For 0 = , the comparison is made against well-known exact analytic results [3,8]. To improve the numerical results further we increase the dimension of the space N until the desired accuracy is reached.…”

“…The S-wave ( 0 = ) Morse potential has been solved analytically [3,8] and its bound states energy is given in a closed form. A brief derivation of this analytic result will be given below for two reasons.…”

“…The Morse potential with 0 ≠ is not exactly solvable and hence our numerical results cannot be checked against exact ones. However many numerical and perturbative results have been published in recent years [8][9][10][11][12][13][14][15][16][17][18]. The most widely used approximation was devised by Pekeris [4] which is based on the expansion of the centrifugal In Table 3 we show the bound states energy of the H 2 molecule for different values of the angular momentum generated by using the Laguerre basis with λ = 40, N = 100 and the model parameters in Table 1.…”

An alternative solution of diatomic molecules

“…The most important analytical methods that have been used in literature to solve these problems are supersymmetry (SUSY) [3,4], Nikiforov-Uvarov (NU) method [5], Pekeris approximation [6], variational method [7], hypervirial perturbation method [8], shifted 1/N expansion (SE) and the modified shifted 1 /N expansion (MSE) [9], exact quantization rule (EQR) [10], perturbative formalism [11][12][13], polynomial solution [14,15], wave function ansatz method [16,17], path integral method [18,19], Lie algebraic method [20][21][22][23], Fourier Grid Hamiltonian method [24], and asymptotic iteration method (AIM) [25,26] to solve the radial Schrödinger equation exactly.…”

Resonant states and pseudospin symmetry in the Dirac-Morse potential

“…The Morse potential is also very useful in expressing the properties of nuclei [29][30][31]. Other applications of Morse potential include the description of the interactions between two atoms in a diatomic molecule [32][33][34][35], the interatomic potential of crystalline solids [36], and the potential for the adsorption of a molecule or atom by a solid surface [37]. This list is far from comprehensive and new applications continue to be found as well.…”