Arbitrary ℓ-State Solutions of the Hyperbolical Potential by the Asymptotic Iteration Method

摘要

The asymptotic iteration method is employed to calculate the any ℓ-state solutions of the Schrödinger equation with the hyperbolical potential by proper approximation to the centrifugal term. Energy eigenvalues and corresponding eigenfunction are obtain analytically. The energy eigenvalues are computed numerically for some values of ℓ and n. Our results are in good agreement with the findings of other methods for short potential range. A straightforward extension to the s-wave (ℓ = 0) and σ _o = 1 cases are also presented.