Extending the Range of Validity for Asymptotic Energy Expansion Method by Padé Approximation

In general, the Asymptotic Energy Expansion method (AEE) produces accurate eigenvalues for higher eigenstates when parameters of the nonleading power terms of the potential are small. However, the ground state and low eigenstates energies calculated from the AEE method are usually inaccurate. Further, when the parameters of the potential are large, accuracy of the AEE method becomes significantly deteriorated. In this paper we show that by applying the Padé approximation, the accuracy of AEE for the ground state and low eigenstates can be significantly improved and eigenenergies for large parameters can be accurately determined.