scholarly journals Application of the Nikiforov-Uvarov Method in Quantum Mechanics

Author(s):  
Cneyt Berkdemir
2006 ◽  
Vol 21 (27) ◽  
pp. 2087-2097 ◽  
Author(s):  
AYŞE BERKDEMIR ◽  
CÜNEYT BERKDEMIR ◽  
RAMAZAN SEVER

Using the Nikiforov–Uvarov method which is based on solving the second-order differential equations, we firstly analyzed the energy spectra and eigenfunctions of the Woods–Saxon potential. In the framework of the PT-symmetric quantum mechanics, we secondly solved the time-independent Schrödinger equation for the PT and non-PT-symmetric version of the potential. It is shown that the discrete energy eigenvalues of the non-PT-symmetric potential consist of the real and imaginary parts, but the PT-symmetric one has a real spectrum. Results are obtained for s-states only.


2020 ◽  
Author(s):  
Ichio Kikuchi ◽  
Akihito Kikuchi

In this essay, we review the Nikiforov-Uvarov method which is used to solve Schro¨dinger equation. We shed light on the algorithm from the viewpoint of algebraic geometry so that we shall the ideas of the latter (such as the resolution of singularity, normalization, primary decomposition of ideal) are lurking behind the algorithm. Besides, we study the application of the introductory D-module theory in this sort of eigenvalue problem and we present an algorithm alternative to the Nikiforov-Uvarov method.


2015 ◽  
Vol 30 (32) ◽  
pp. 1550193 ◽  
Author(s):  
H. I. Ahmadov ◽  
Sh. I. Jafarzade ◽  
M. V. Qocayeva

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 concept 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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