In this work, the analytical solution of the radial Schrödinger equation for the Woods-Saxon potential is presented. In our calculations, we have applied the Nikiforov-Uvarov method by using the Pekeris approximation to the centrifugal potential for arbitrary l states. The bound state energy eigenvalues and corresponding eigenfunctions are obtained for various values of n and l quantum numbers.

The radial part of the Klein-Gordon equation for the Woods-Saxon potential is solved. In our calculations, we have applied the Nikiforov-Uvarov method by using the Pekeris approximation to the centrifugal potential for any l states. The exact bound state energy eigenvalues and the corresponding eigenfunctions are obtained for a particle bound on the various values of the quantum numbers n and l.

The analytical solution of the Schrödinger equation for the Manning-Rosen potential plus a ringshaped like potential is obtained by applying the Nikiforov-Uvarov method by using the improved approximation scheme to the centrifugal potential for arbitrary l states. The energy levels are worked out and the corresponding normalized eigenfunctions are obtained in terms of orthogonal polynomials for arbitrary l states.

In this paper, the analytical solutions of the [Formula: see text]-dimensional hyper-radial Schrödinger equation are studied in great detail for the Hulthén potential. Within the framework, a novel improved scheme to surmount centrifugal term, the energy eigenvalues and corresponding radial wave functions are found for any [Formula: see text] orbital angular momentum case within the context of the Nikiforov–Uvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. In this way, based on these methods, the same expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transforming each other is demonstrated. The energy levels are worked out and the corresponding normalized eigenfunctions are obtained in terms of orthogonal polynomials for arbitrary [Formula: see text] states for [Formula: see text]-dimensional space.

The analytical solution of the modified radial Schrödinger equation for the Hulthén potential is obtained within ordinary quantum mechanics by applying the Nikiforov-Uvarov method and supersymmetric quantum mechanics by applying the shape invariance consept that was introduced by Gendenshtein method by using the improved approximation scheme to the centrifugal potential for arbitrary l states. The energy levels are worked out and the corresponding normalized eigenfunctions are obtained in terms of orthogonal polynomials for arbitrary l states.

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In this paper the asymptotic distributions are exactly solved for linearly independent solutions considering problem of the second order and for the coefficients of asymptotic destribution the recurent formulas are obtained. Further, using obtained recurent formulas the neccessary and sufficient conditions almost regularity of spectral problem for the equation of the second order is proved. *

In this paper we investigate distribution of zeros for only quasipolynom and obtain exactly lower-bound for their modulus.