Exact bound states for the central fraction power potentialV(r)=α/r 1/2+β/r 3/2

1994 ◽  
Vol 109 (3) ◽  
pp. 311-314 ◽  
Author(s):  
S. K. Bose
Keyword(s):  
Bound States ◽  
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 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.

Exact bound states of some N‐body systems with two‐ and three‐body forces

1973 ◽  
Vol 14 (2) ◽  
pp. 182-184 ◽  
Author(s):  
F. Calogero ◽  
C. Marchioro
Keyword(s):  
Bound States ◽  
Exact Bound ◽  
Body Forces ◽  
Three Body

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.

scholarly journals A Novel Exactly Theoretical Solvable of Bound States of the Dirac-Kratzer-Fues Problem with Spin and Pseudo-Spin Symmetry

2016 ◽  
Vol 10 ◽  
pp. 8-22
Author(s):  
Abdelmadjid Maireche
Keyword(s):  
Dirac Equation ◽  
Bound States ◽  
Star Product ◽  
Three Dimensional ◽  
Spin Symmetry ◽  
Hamiltonian Operator ◽  
Bound State ◽  
Exact Bound ◽  
Quantum Numbers ◽  
Quantum Symmetries

New exact bound state solutions of the deformed radial upper and lower components of Dirac equation and corresponding Hermitian anisotropic Hamiltonian operator are studied for the modified Kratzer-Fues potential (m.k.f.) potential by using Bopp’s shift method instead to solving deformed Dirac equation with star product. The corrections of energy eigenvalues are obtained by applying standard perturbation theory for interactions in one-electron atoms. Moreover, the obtained corrections of energies are depended on two infinitesimal parameters (θ,χ), which induced by position-position noncommutativity, in addition to the discreet nonrelativistic atomic quantum numbers: (j=l±1/1,s=±1/2,landm) and we have also shown that, the usual relativistic states in ordinary three dimensional spaces are canceled and has been replaced by new degenerated 2(2l+1) sub-states in the extended quantum symmetries (NC: 3D-RS).

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