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

10.5772/33510 ◽  
2012 ◽  
Author(s):  
Cneyt Berkdemir
Keyword(s):  
Quantum Mechanics ◽  
Uvarov Method

scholarly journals EIGENVALUES AND EIGENFUNCTIONS OF WOODS–SAXON POTENTIAL IN PT-SYMMETRIC QUANTUM MECHANICS

2006 ◽  
Vol 21 (27) ◽  
pp. 2087-2097 ◽  
Author(s):  
AYŞE BERKDEMIR ◽  
CÜNEYT BERKDEMIR ◽  
RAMAZAN SEVER
Keyword(s):  
Quantum Mechanics ◽  
Real Spectrum ◽  
Saxon Potential ◽  
Eigenvalues And Eigenfunctions ◽  
Discrete Energy ◽  
Energy Eigenvalues ◽  
Symmetric Quantum ◽  
Symmetric Version ◽  
Uvarov Method ◽  
S States

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.

scholarly journals Explanation of Nikiforov-Uvarov method in quantum mechanics – with a view toward algebraic geometry

2020 ◽  
Author(s):  
Ichio Kikuchi ◽  
Akihito Kikuchi
Keyword(s):  
Quantum Mechanics ◽  
Algebraic Geometry ◽  
Eigenvalue Problem ◽  
Primary Decomposition ◽  
Module Theory ◽  
Dinger Equation ◽  
Resolution Of Singularity ◽  
Uvarov Method ◽  
Shed Light

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.

scholarly journals Analytical solutions of the Schrödinger equation for the Hulthén potential within SUSY quantum mechanics

2015 ◽  
Vol 30 (32) ◽  
pp. 1550193 ◽  
Author(s):  
H. I. Ahmadov ◽  
Sh. I. Jafarzade ◽  
M. V. Qocayeva
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Energy Levels ◽  
Hulthén Potential ◽  
Shape Invariance ◽  
Hulthen Potential ◽  
Radial Schrödinger Equation ◽  
Uvarov Method ◽  
Ordinary Quantum

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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