Eigenenergies and oscillator strengths for the Hulthén potential

The generalized pseudospectral approach to the bound states of the Hulthén and the Yukawa potentials

“…These values from [18] are given in parentheses. Majority of the previous works have dealt with the weak coupling regions.…”

“…As already mentioned, these states do not offer exact analytical results and a large number of attempts have been made over the years, e.g., the variational as well as numerical integration [18], strong-coupling expansion [42], supersymmetric quantum mechanics [29], parameter-free wave function approach based on the local properties such as the cusp conditions [31], etc., in addition to some of the methods which also dealt with the ℓ = 0 case such as [16,19,24,28,31]. Other works include [7,43,44] and the best results are quoted here for comparison.…”

“…Many formally attractive and efficient formalisms have been proposed for accurate determination of the eigenvalues, eigenfunctions as well as for the values of the critical screening parameters differing in complexity, accuracy and efficiency. The most notable of these are the variational calculations employing a multitude of basis functions [14][15][16][17][18]12], combined Padé approximation and perturbation theory [19][20][21], shifted 1/N approximation along with many of its variants [22][23][24][25][26][27], dynamical-group approach [28], supersymmetric quantum mechanics [29], numerical calculations [30][31]18] and other works [32][33].…”

Application of the Nikiforov-Uvarov Method in Quantum Mechanics

“…The Hulthen potential has been used in several branches of physics such as nuclear and particle, atomic, molecular and chemical physics (Durand & Durand, 1981;Xu et al, 2006;Bitensky et al, 1997;Jia et al, 2000;Olson & Micha, 1978). Moreover, its discrete and continuum states have been studied by a variety of techniques such as the supersymmetry and shape invariance property (Varshni, 1990;Filho & Ricotta, 1995;Qian et al, 2002). The solution of the SE for a particle in the Hulthen potential can not be obtained exactly for the case of ℓ = 0 whereas we have an exact solution for the case of ℓ = 0, namely s-wave solution (Flügge, 1971).…”

Approximate analytical solutions of scattering states for Klein-Gordon equation with Hulthén potentials for nonzero angular momentum

“…For the case = 0, the Hulthén potential cannot be exactly solved. In the nonrelativistic case, for nonzero angular momentum, several techniques were used to obtain approximate solutions, a number of methods have been used to find the boundstate energy eigenvalues numerically [9,10] and quasianalytically, such as the variational [9,11], perturbation [12], shifted 1/N expansion [13,14], SUSYQM [15,16], and AIM [17] methods. In the relativistic case, DominguezAdame [18], Chetouani et al [19], and Talukdar et al [20] …”