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Asymptotic iteration method for eigenvalue problems

An asymptotic iteration method for solving second-order homogeneous linear differential equations of the form y'' = λ0(x)y' + s0(x)y is introduced, where λ0(x) ≠ 0 and s0(x) are C∞ functions.… Expand

Integrals containing confluent hypergeometric functions with applications to perturbed singular potentials

We show that many integrals containing products of confluent hypergeometric functions follow directly from one single integral that has a very simple formula in terms of Appell's double series F2. We… Expand

A geometrical theory of energy trajectories in quantum mechanics

- R. Hall
- Physics
- 1 February 1983

Suppose f(r) is an attractive central potential of the form f(r)=∑ki=1 g(i)( f(i)(r)), where {f(i)} is a set of basis potentials (powers, log, Hulthen, sech2) and {g(i)} is a set of smooth increasing… Expand

Iterative solutions to the Dirac equation

We consider a single particle which is bound by a central potential and obeys the Dirac equation in d dimensions. We first apply the asymptotic iteration method to recover the known exact solutions… Expand

Physical applications of second-order linear differential equations that admit polynomial solutions

- H. Ciftci, R. Hall, N. Saad, Ebubekir Dogu
- Mathematics
- 2 September 2010

In this paper conditions for the second-order linear differential equation to have polynomial solutions are given. Several applications of these results to Schrödinger's equation are discussed.… Expand

Kinetic potentials in quantum mechanics

- R. Hall
- Physics
- 1 September 1984

Suppose that the Hamiltonian H=−Δ+vf(r) represents the energy of a particle which moves in an attractive central potential and obeys nonrelativistic quantum mechanics. The discrete eigenvalues… Expand

Construction of exact solutions to eigenvalue problems by the asymptotic iteration method

We apply the asymptotic iteration method (AIM) (Ciftci, Hall and Saad 2003 J. Phys. A: Math. Gen. 36 11807) to solve new classes of second-order homogeneous linear differential equation. In… Expand

Criterion for polynomial solutions to a class of linear differential equations of second order

We consider the differential equations y'' = λ0(x)y' + s0(x)y, where λ0(x), s0(x) are C∞-functions. We prove (i) if the differential equation has a polynomial solution of degree n > 0, then δn =… Expand

Schrödinger spectrum generated by the Cornell potential

Abstract The eigenvalues Ednl (a, c) of the d-dimensional Schrödinger equation with the Cornell potential V(r) = −a/r + c r, a, c > 0 are analyzed by means of the envelope method and the asymptotic… Expand

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