Studies on bound-state spectra of Manning–Rosen potential

Abstract

Accurate ro-vibrational energies, eigenfunctions, radial densities, expectation values are presented for the exponential-type Manning-Rosen (MR) potential. Bound states accurate up to ten significant figure are obtained by employing a simple, reliable generalized pseudospectral method.All 55 eigenstates with n ≤ 10 are treated for arbitrary values of potential parameters, covering a wide range of interaction, through a non-uniform, optimal spatial radial discretization. A detailed investigation has been made on energy changes with respect to screening and other potential parameters. A systematic estimation of critical screening parameters are given for these eigenstates.Special emphasis has been given to higher states and in the vicinity of critical screening region.A thorough comparison with literature results is made wherever possible. This surpasses the accuracy of all other existing methods currently available. Several new states are reported for the first time. In short, a simple, efficient scheme for accurate calculation of this and other molecular potentials is offered. notable approaches are: a super-symmetric shape invariance formalism in conjunction with function analysis method [11], an approximation for centrifugal term different from the usual one used above, containing 3 adjustable parameters in it [12], yet another alternative approximation to the centrifugal potential within a Nikiforov-Uvarov method [13], the Duru-Kleinert method of path-integral formalism [14], Laguerre and oscillator bases to tridiagonalize the reference Hamiltonian and subsequently a Gauss quadrature approach for

Information Entropies for H2 and ScF Diatomic Molecules with Deng- Fan-Eckart Potential

“…This study will offer more information in the applications to semiconductors and quantum dots. Information entropies have been investigated for scaling behavior properties [26][27][28], confined systems [29][30][31][32], shape effect of quantum heterostructures [33], among others [34][35][36][37][38][39][40][41]. In recent times, there are very little research works on information theory with exponential type potentials, and to the best of our knowledge, no application of diatomic molecules for exponential type potential has been investigated and hence the motivation of this study.…”

Bound and scattering states for a hyperbolic‐type potential in view of a new developed approximation

“…There are a few method to solve the second‐order differential equation: function analysis method, exact quantization rule method, supersymmetric quantum mechanics method, factorization method, asymptotic iteration method, generalized pseudospectral method, pseudospectral method, variational method, perturbation method, shifted 1∕ N expansion method . These methods have some advantages and/or disadvantages to find exact eigenvalues equation and eigenfunctions according to each other.…”

Application of the Frobenius Method to the Schr？dinger Equation for a Spherically Symmetric Hyperbolic Potential

“…It is well known that the exact solution of the Schrödinger Equation (SE) plays a vital role in quantum mechanics, and solving this equation is still an interesting work in the existing literature [1]- [6]. Generally, the SE is very difficult to solve for most physical central potentials [7] [8] [9]. It is for this reason that approximation and numerical methods are frequently used to arrive at the solution [6] [10]- [15].…”