Exact bound states for the central fraction power singular potential $$V(r) = \alpha r^{2/3} + \beta r^{ - 2/3} + \gamma r^{ - 4/3} $$ .

1994 ◽  
Vol 109 (11) ◽  
pp. 1217-1220 ◽  
Author(s):  
S. K. Bose
Keyword(s):  
Bound States ◽  
Singular Potential ◽  
Exact Bound

scholarly journals Bound states of an inverse-cube singular potential: A candidate for electron-quadrupole binding

2019 ◽  
Vol 34 (28) ◽  
pp. 1950223 ◽  
Author(s):  
A. D. Alhaidari
Keyword(s):  
Bound States ◽  
Recursion Relation ◽  
Singular Potential ◽  
Electric Quadrupole ◽  
Exact Bound ◽  
Short Range Potential ◽  
Integrable Functions ◽  
Solution Energy ◽  
Expansion Coefficients ◽  
Square Integrable Functions

We use the Tridiagonal Representation Approach (TRA) to obtain exact bound states solution (energy spectrum and wave function) of the Schrödinger equation for a three-parameter short-range potential with [Formula: see text], [Formula: see text] and [Formula: see text] singularities at the origin. The solution is a finite series of square-integrable functions with expansion coefficients that satisfy a three-term recursion relation. The solution of the recursion is a non-conventional orthogonal polynomial with discrete spectrum. The results of this work could be used to study the binding of an electron to a molecule with an effective electric quadrupole moment which has the same [Formula: see text] singularity.

scholarly journals On Scattering and Bound States for a Singular Potential

1970 ◽  
Vol 43 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Erasmo Ferreira ◽  
Javier Sesma ◽  
Pedro L. Torres
Keyword(s):  
Bound States ◽  
Singular Potential

scholarly journals Exact bound states in volcano potentials

2007 ◽  
Vol 363 (5-6) ◽  
pp. 369-373 ◽  
Author(s):  
Ratna Koley ◽  
Sayan Kar
Keyword(s):  
Bound States ◽  
Exact Bound

scholarly journals BOUND-STATES OF A SEMI-RELATIVISTIC EQUATION FOR THE ${\cal PT}$-SYMMETRIC GENERALIZED HULTHÉN POTENTIAL BY THE NIKIFOROV–UVAROV METHOD

2008 ◽  
Vol 17 (06) ◽  
pp. 1107-1123 ◽  
Author(s):  
SAMEER M. IKHDAIR ◽  
RAMAZAN SEVER
Keyword(s):  
Bound States ◽  
Relativistic Equation ◽  
Hulthén Potential ◽  
Exact Bound ◽  
Hulthen Potential ◽  
Hypergeometric Type ◽  
Linear Differential ◽  
The One ◽  
Uvarov Method ◽  
S States

The one-dimensional semi-relativistic equation has been solved for the [Formula: see text]-symmetric generalized Hulthén potential. The Nikiforov–Uvarov (NU) method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type, is used to obtain exact energy eigenvalues and corresponding eigenfunctions. We have investigated the positive and negative exact bound states of the s-states for different types of complex generalized Hulthén potentials.

scholarly journals EXACT BOUND STATES OF THE D-DIMENSIONAL KLEIN–GORDON EQUATION WITH EQUAL SCALAR AND VECTOR RING-SHAPED PSEUDOHARMONIC POTENTIAL

2008 ◽  
Vol 19 (09) ◽  
pp. 1425-1442 ◽  
Author(s):  
SAMEER M. IKHDAIR ◽  
RAMAZAN SEVER
Keyword(s):  
Bound States ◽  
Gordon Equation ◽  
Energy Levels ◽  
Three Dimensional ◽  
Bound State ◽  
Exact Bound ◽  
Pseudoharmonic Potential ◽  
Klein Gordon ◽  
Equal Scalar ◽  
Klein Gordon Equation

We present the exact solution of the Klein–Gordon equation in D-dimensions in the presence of the equal scalar and vector pseudoharmonic potential plus the ring-shaped potential using the Nikiforov–Uvarov method. We obtain the exact bound state energy levels and the corresponding eigen functions for a spin-zero particles. We also find that the solution for this ring-shaped pseudoharmonic potential can be reduced to the three-dimensional (3D) pseudoharmonic solution once the coupling constant of the angular part of the potential becomes zero.

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