Approximate solutions of Schrödinger equation for Eckart potential with centrifugal term

Abstract

The approximate analytical solutions of the Schrödinger equation for the Eckart potential are presented for the arbitrary angular momentum by using a new approximation of the centrifugal term. The energy eigenvalues and the corresponding wavefunctions are obtained for different values of screening parameter. The numerical examples are presented and the results are in good agreement with the values in the literature. Three special cases, i.e., s-wave, ξ = λ = 1, and β = 0, are investigated.

Arbitrary l-state solutions of the Schrödinger equation for the Eckart potential with an improved approximation of the centrifugal term

“…when the α = 1/ parameter increases, it is evident that present results are in better agreement with those obtained numerically than the previous ones. The accuracy of the present model results in up to 10-300 times better agreement than the estimations provided by [12]. Consequently, it confirms the validity and usefulness of our approximation scheme.…”

“…Our results were compared with those obtained numerically by Lucha and Schöberl [16] with the help of the MATHEMATICA package and those obtained by Tașkin and Koçak [12] . All results are shown in Table 1 a We found two misprints in Table 1 and 2 of Ref.…”

“…All results are shown in Table 1 a We found two misprints in Table 1 and 2 of Ref. [12] which are corrected here. when the α = 1/ parameter increases, it is evident that present results are in better agreement with those obtained numerically than the previous ones.…”

“…In the next Section, applying the improved approximate scheme to the centrifugal term we present the bound state solutions and the normalized radial wave functions of the Eckart-like potential for the arbitrary angular momentum number. In Section 3, our results are compared with the best results published by Tașkin et al [12] and the accurate numerical ones [16]. Concluding remarks are given in Section 4.…”

“…It means that the Greene and Aldrich approximation scheme for the centrifugal term is valid only when the potential parameter is large. Recently, Tașkin and Koçak [12] investigated the same model using an approximation scheme similar to (1). They obtained quite accurate results, particularly for small values of the screening parameter , but with coefficients (denoted there as λ and ξ) taken as adjustable parameters.…”