An Improvement of the Asymptotic Iteration Method for Exactly Solvable Eigenvalue Problems

Abstract

We derive a formula that simplifies the original asymptotic iteration method formulation to find the energy eigenvalues for the analytically solvable cases. We then show that there is a connection between the asymptotic iteration and the Nikiforov--Uvarov methods, which both solve the second order linear ordinary differential equations analytically.

RevTex4, 8 pages

References in corpus (9)

• Asymptotic iteration method for eigenvalue problems
• Construction of exact solutions to eigenvalue problems by the asymptotic iteration method
• Arbitrary l-state solutions of the rotating Morse potential by the asymptotic iteration method
• Asymptotic Iteration Method Solutions to the Relativistic Duffin-Kemmer-Petiau Equation
• Exact solutions of the Schrodinger equation with non central potential by Nikiforov Uvarov method
• Exact analytical solution to the relativistic Klein-Gordon equation with non-central equal scalar and vector potentials
• Criterion for polynomial solutions to a class of linear differential equation of second order
• Solution of the Radial Schrödinger Equation for the Potential Family $V(r)=\frac{A}{r^2}-\frac{B}{r}+C{r}^{\kappa }$ using the Asymptotic Iteration Method
• A search on the Nikiforov-Uvarov formalism

Cited by in corpus (11)

• Analytical solutions of the Bohr Hamiltonian with the Morse potential
• Bohr Hamiltonian with Hulth?en plus Ring shaped potential for triaxial nuclei
• Electric quadrupole transitions of the Bohr Hamiltonian with the Morse potential
• Closed analytical solutions of Bohr Hamiltonian with Manning-Rosen potential model
• Electric quadrupole transitions of the Bohr Hamiltonian with Manning-Rosen potential
• Davydov-Chaban Hamiltonian with deformation-dependent mass term for γ = 30°
• Bohr Hamiltonian with Hulthen plus ring-shaped potential for triaxial nuclei with deformation-dependent mass term
• Spin Averaged Mass Spectrum of Heavy Quarkonium via Asymptotic Iteration Method
• Energy spectrum of a generalized Scarf potential using the Asymptotic Iteration Method and the Tridiagonal Representation Approach
• Generalized quantum mechanical two Coulomb centers problem (Demkov problem)
• AIMpy: A Python code to solve Schrödinger-like equations with the asymptotic iteration method