Study of a confined hydrogen‐like atom by the asymptotic iteration method

Abstract

Abstract. The asymptotic iteration method (AIM) is used to obtain both special exact solutions and general approximate solutions for a Hydrogen-like atom confined in a spherical box of arbitrary radius R. Critical box radii, at which states are no longer bound, are also calculated. The results are compared with those in the literature.

Spherical confinement of coulombic systems inside an impenetrable box: H atom and the Hulthén potential

“…For all values of radii, present energies for both states completely agree with the quoted values, for up to the precision they are presented in . Some other very accurate results are also found, for example, the series method asymptotic iteration method . Former results exist for both states, while same for the latter offers only 2 s states.…”

“…[34] Some other very accurate results are also found, for example, the series method [33] asymptotic iteration method. [32] Former results exist for both states, while same for the latter offers only 2s states. For all instances, our energies are seen to either agree completely with these, or differ only in the last place of decimal quoted.…”

“…Approximate analytical formulas for CHA eigenvalues were derived using Vawter's cothz method, [14] joint perturbation method, and Pad e approximation, [15,16] Wentzel-Kramers-Brillouin (WKB) method. [17] Some other attempts are: a combined hypervirial theorem and perturbation theory, [18] a variational boundary perturbation method with appropriate cut-off function [19,20] along with its variants, [21,22] by extending a power-series solution, [23] originally proposed for free quantum systems, to confined case, [24] selfconsistent solution [25] of relevant Kohn-Sham equation within the broad domain of density functional theory, variational perturbation theory, [26] variational method in conjunction with super-symmetric quantum mechanics, [27,28] Rayleigh-Schr€ odinger perturbation theory, [29] Lie algebraic treatment, [29] Lagrange-mesh method, [30] searching the zeros of hypergeometric function, [31] asymptotic iteration method, [32] and so forth. So far, the most accurate calculations are those based on formal solution of confluent hypergeometric function and series method.…”

Information‐entropic measures in free and confined hydrogen atom

“…Effect of compression on energy levels of ground and excited states, as well as other properties like hyperfine splitting constant, dipole shielding factor, nuclear magnetic screening constant, pressure, static, and dynamic polarizability, were examined . Numerous theoretical methods varying in complexity, sophistication were employed; a selected set includes perturbation theory, Padé approximation, WKB method, Hypervirial theorem, power‐series solution, super‐symmetric quantum mechanics, Lie algebra, Lagrange‐mesh method, asymptotic iteration method, generalized pseudo‐spectral method, and so forth and references therein. Exact solutions are expressible in terms of Kummer M‐function (confluent hypergeometric).…”

Energy Spectra of tightly Confined Systems

“…For such cases, there are some analytical and numerical approximation methods such as 1/ expansion (Bag, Panja, & Dutt, 1992), supersymmetry (Morales, 2004), Pekeris approximation (Pekeris, 1934), variational methods (Montgomery, 2001(Montgomery, , 2011, and asymptotic iteration methods (Ciftci, Hall, & Saad, 2009) to obtain the energy eigenvalues and eigenfunctions with this type of boundary conditions. Another technique used to find exact solutions of quantum systems is the Nikiforov-Uvarov method (Nikiforov & Uvarov, 1988;Szego, 1975), which is now used often but for non confined systems by many authors.For detailed applications and applicability of the Nikiforov-Uvarov method in quantum mechanics, the reader may refer to (Berkdemir, 2012).…”