An asymptotic interation method for solving second-order homogeneous linear differential equations of the form y'' = lambda(x) y' + s(x) y is introduced, where lambda(x) \neq 0 and s(x) are C-infinity functions. Applications to Schroedinger type problems, including some with highly singular potentials, are presented.

https://arxiv.org/pdf/math-ph/0309066.pdf

Asymptotic iteration method for eigenvalue problems

Enthalpy of gaseous phosphorus dimer

In this paper we use the Nikiforov-Uvarov method to obtain the approximate solutions for the Klein-Gordon equation with the deformed five-parameter exponential-type potential (DFPEP) model. We also obtain solutions for the Schrodinger equation in the presence of DFPEP in non-relativistic limits. In addition, we calculate in the non-relativistic limits thermodynamics properties, such as vibrational mean energy U, free energy F and the specific heat capacity C. Special cases of the potential are also discussed.

Klein-Gordon equation particles in exponential-type molecule potentials and their thermodynamic properties in D dimensions

The approximate analytical solutions of the radial Schrodinger equation have been obtained with a newly proposed potential called Hellmann–Kratzer potential. The potential is a superposition of Hellmann potential and modified Kratzer potential. The Hellmann–Kratzer potential actually comprises of three different potentials which include Yukawa potential, Coulomb potential and Kratzer potential. The aim of combining these potentials is to have a wide application. The energy eigenvalue and the corresponding wave function are calculated in a closed and compact form using the Nikiforov–Uvarov method. The energy equation for some potentials such as Kratzer, Hellmann, Yukawa and Coulomb potentials has also been obtained by varying some potential parameters. Our results excellently agree with the already existing literature. Some numerical results have been computed. We have plotted the behaviour of the energy eigenvalues with different potential parameters and also reported on the numerical result.

Any l-state solutions of the Schrodinger equation interacting with Hellmann–Kratzer potential model

Improved Pöschl–Teller potential energy model for diatomic molecules

In quantum mechanics, the study of exact solutions of relativistic and non-relativistic equation with different potentials plays a significant role in Physics. The bound state solution of Klein Gordon equation (KGE) is of great important in nuclear and high energy physics. Klein Gordon equation is a relativistic wave equation that describes spinzero particles. It contains of two major objects, the vector potential V(r) and the scalar potential S(r). In D-dimension, the Klein Gordon equation is written as

Solution of Klein Gordon Equation for Some Diatomic Molecules with New Generalized Morse-like Potential Using SUSYQM

In this paper, we present solutions of the Klein-Gordon equation for the improved Manning—Rosen potential for arbitrary l state in d-dimensions using the supersymmetric shape invariance method. We obtained the energy levels and the corresponding wave functions expressed in terms of Jacobi polynomial in a closed form for arbitrary l state. We also calculate the oscillator strength for the potential.

Approximate solutions of Klein-Gordon equation with improved Manning-Rosen potential in D-dimensions using SUSYQM

Quantum information‐theoretic measures for the static screened Coulomb potential

We used a tool of conventional Nikiforov-Uvarov method to determine bound state solutions of Schrodinger equation with quantum interaction potential called Hulthen-Yukawa inversely quadratic potential (HYIQP) We obtained the energy eigenvalues and the total normalized wave function We employed Hellmann-Feynman Theorem (HFT) to compute expectation values , , , and for four different diatomic molecules: hydrogen molecule (H2), lithium hydride molecule (LiH), hydrogen chloride molecule (HCl), and carbon (II) oxide molecule The resulting energy equation reduces to three well-known potentials which are as follows: Hulthen potential, Yukawa potential, and inversely quadratic potential The bound state energies for Hulthen and Yukawa potentials agree with the result reported in existing literature We obtained the numerical bound state energies of the expectation values by implementing MATLAB algorithm using experimentally determined spectroscopic constant for the different diatomic molecules We developed mathematica programming to obtain wave function and probability density plots for different orbital angular quantum number

/pdf/approximate-solutions-of-schrodinger-equation-with-some-34mp48a31j.pdf

Approximate Solutions of Schrodinger Equation with Some Diatomic Molecular Interactions Using Nikiforov-Uvarov Method

Thermodynamic properties and bound state solutions of Schrodinger equation with Mobius square plus screened-Kratzer potential using Nikiforov-Uvarov method

Cecilia N. Isonguyo

Papers

Solution of Klein Gordon Equation for Some Diatomic Molecules with New Generalized Morse-like Potential Using SUSYQM

Approximate solutions of Klein-Gordon equation with improved Manning-Rosen potential in D-dimensions using SUSYQM

Quantum information‐theoretic measures for the static screened Coulomb potential

Approximate Solutions of Schrodinger Equation with Some Diatomic Molecular Interactions Using Nikiforov-Uvarov Method

Thermodynamic properties and bound state solutions of Schrodinger equation with Mobius square plus screened-Kratzer potential using Nikiforov-Uvarov method