SOLUTIONS OF THE SCHRODINGER EQUATION WITH INVERSELY QUADRATIC YUKAWA PLUS WOODS-SAXON POTENTIAL USING NIKIFOROV-UVAROV METHOD

2015 ◽  
Vol 8 (2) ◽  
pp. 2094-2098
Author(s):  
Benedict Ita ◽  
A. I. Ikeuba ◽  
O. Obinna
Keyword(s):  
State Energy ◽  
Jacobi Polynomials ◽  
Bound State ◽  
Negative Energy ◽  
Saxon Potential ◽  
Energy Eigenvalues ◽  
Eigen Values ◽  
Uvarov Method ◽  
Special Case ◽  
Nu Method

The solutions of the SchrÓ§dinger equation with inversely quadratic Yukawa plus Woods-Saxon potential (IQYWSP) have been presented using the parametric Nikiforov-Uvarov (NU) method. The bound state energy eigenvalues and the corresponding un-normalized eigen functions are obtained in terms of Jacobi polynomials. Also, a special case of the potential has been considered and its energy eigen values obtained. The result of the work could be applied to molecules moving under the influence of IQYWSP potential as negative energy eigenvalues obtained indicate a bound state system.

scholarly journals ANALYTICAL SOLUTIONS OF THE SCHRÖDINGER EQUATION WITH THE WOODS–SAXON POTENTIAL FOR ARBITRARY l STATE

2009 ◽  
Vol 18 (03) ◽  
pp. 631-641 ◽  
Author(s):  
V. H. BADALOV ◽  
H. I. AHMADOV ◽  
A. I. AHMADOV
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
State Energy ◽  
Bound State ◽  
Saxon Potential ◽  
Energy Eigenvalues ◽  
Quantum Numbers ◽  
Radial Schrödinger Equation ◽  
Uvarov Method ◽  
Pekeris Approximation

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.

REAL SPECTRUM OF NON-HERMITIAN HAMILTONIANS FOR HULTHÉN POTENTIAL

2008 ◽  
Vol 23 (25) ◽  
pp. 2077-2084 ◽  
Author(s):  
SANJIB MEYUR ◽  
S. DEBNATH
Keyword(s):  
State Energy ◽  
Jacobi Polynomials ◽  
Bound State ◽  
Real Spectrum ◽  
Eigenvalues And Eigenfunctions ◽  
Hulthén Potential ◽  
Exact Bound ◽  
Energy Eigenvalues ◽  
Hulthen Potential ◽  
Uvarov Method

The non-Hermitian Hamiltonians of the type [Formula: see text] is solved for the generalized Hulthén potential in terms of Jacobi polynomials by using Nikiforov–Uvarov method. The exact bound-state energy eigenvalues and eigenfunctions are presented.

scholarly journals ANY l-STATE ANALYTICAL SOLUTIONS OF THE KLEIN–GORDON EQUATION FOR THE WOODS–SAXON POTENTIAL

2010 ◽  
Vol 19 (07) ◽  
pp. 1463-1475 ◽  
Author(s):  
V. H. BADALOV ◽  
H. I. AHMADOV ◽  
S. V. BADALOV
Keyword(s):  
State Energy ◽  
Gordon Equation ◽  
Bound State ◽  
Nonrelativistic Limit ◽  
Saxon Potential ◽  
Bound State Energy ◽  
Klein Gordon ◽  
Uvarov Method ◽  
Pekeris Approximation ◽  
Klein Gordon Equation

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 on the various values of the quantum numbers n and l. The nonrelativistic limit of the bound state energy spectrum was also found.

EXACT SOLUTIONS OF DIRAC EQUATION WITH HARTMANN POTENTIAL BY NIKIFOROV–UVAROV METHOD

2010 ◽  
Vol 19 (11) ◽  
pp. 2189-2197 ◽  
Author(s):  
M. HAMZAVI ◽  
H. HASSANABADI ◽  
A. A. RAJABI
Keyword(s):  
Dirac Equation ◽  
State Energy ◽  
Bound State ◽  
Energy Eigenvalues ◽  
Dirac Particles ◽  
Uvarov Method ◽  
Spinor Wave ◽  
Polar Parts ◽  
Component Spinor ◽  
Hartmann Potential

We investigate the exact solution of the Dirac equation for the Hartmann potential. The radial and polar parts of the Dirac equation are solved by Nikiforov–Uvarov method. The bound state energy eigenvalues and the corresponding two-component spinor wave functions of the Dirac particles are obtained.

scholarly journals BOUND STATE SOLUTIONS OF SCHRÖDINGER EQUATION FOR A MORE GENERAL EXPONENTIAL SCREENED COULOMB POTENTIAL VIA NIKIFOROVUVAROV METHOD

2018 ◽  
Vol 35 (3) ◽  
pp. 103
Author(s):  
Benedict Iserom Ita ◽  
P. Ekuri ◽  
Idongesit O. Isaac ◽  
Abosede O. James
Keyword(s):  
Angular Momentum ◽  
Schrödinger Equation ◽  
Coulomb Potential ◽  
Schrodinger Equation ◽  
Jacobi Polynomials ◽  
Bound State ◽  
Energy Eigenvalues ◽  
Bounded State ◽  
Screened Coulomb Potential ◽  
Nu Method

The arbitrary angular momentum solutions of the Schrödinger equation for a diatomic molecule with the general exponential screened coulomb potential of the form V(r) = (− a / r){1+ (1+ br )e−2br } has been presented. The energy eigenvalues and the corresponding eigenfunctions are calculated analytically by the use of Nikiforov-Uvarov (NU) method which is related to the solutions in terms of Jacobi polynomials. The bounded state eigenvalues are calculated numerically for the 1s state of N2 CO and NO

PSEUDOSPIN AND SPIN SYMMETRY FOR THE RING-SHAPED GENERALIZED HULTHÉN POTENTIAL

2010 ◽  
Vol 25 (21) ◽  
pp. 4067-4079 ◽  
Author(s):  
OKTAY AYDOĞDU ◽  
RAMAZAN SEVER
Keyword(s):  
State Energy ◽  
Spin Symmetry ◽  
Bound State ◽  
Wave Functions ◽  
Relativistic Energy ◽  
Hulthén Potential ◽  
Energy Eigenvalues ◽  
Hulthen Potential ◽  
Dependent Part ◽  
Uvarov Method

We obtain the bound state energy eigenvalues and the corresponding wave functions of the Dirac particle for the generalized Hulthén potential plus a ring-shaped potential with pseudospin and spin symmetry. The Nikiforov–Uvarov method is used in the calculations. Contribution of the angle-dependent part of the potential to the relativistic energy spectra are investigated. In addition, it is shown that the obtained results coincide with those available in the literature.

Effect of the velocity-dependent potentials on the energy eigenvalues of the Morse potential

Open Physics ◽  
2012 ◽  
Vol 10 (4) ◽  
Author(s):  
Asim Soylu ◽  
Orhan Bayrak ◽  
Ismail Boztosun
Keyword(s):  
Morse Potential ◽  
State Energy ◽  
Bound State ◽  
Quantum States ◽  
Bound State Energy ◽  
Energy Eigenvalues ◽  
Dependent Term ◽  
Oscillator Type ◽  
Dependent Potential ◽  
Pekeris Approximation

AbstractWe investigate the effect of the isotropic velocity-dependent potentials on the bound state energy eigenvalues of the Morse potential for any quantum states. When the velocity-dependent term is used as a constant parameter, ρ(r) = ρ 0, the energy eigenvalues can be obtained analytically by using the Pekeris approximation. When the velocity-dependent term is considered as an harmonic oscillator type, ρ(r) = ρ 0 r 2, we show how to obtain the energy eigenvalues of the Morse potential without any approximation for any n and ℓ quantum states by using numerical calculations. The calculations have been performed for different energy eigenvalues and different numerical values of ρ 0, in order to show the contribution of the velocity-dependent potential on the energy eigenvalues of the Morse potential.

scholarly journals EXACT SOLUTION OF THE SCHRÖDINGER EQUATION FOR THE MODIFIED KRATZER'S MOLECULAR POTENTIAL WITH POSITION-DEPENDENT MASS

2008 ◽  
Vol 17 (07) ◽  
pp. 1327-1334 ◽  
Author(s):  
RAMAZÀN SEVER ◽  
CEVDET TEZCAN
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
State Energy ◽  
Bound State ◽  
Bound State Energy ◽  
Energy Eigenvalues ◽  
Molecular Potential ◽  
Dependent Mass ◽  
Morse Potentials ◽  
Position Dependent Mass

Exact solutions of Schrödinger equation are obtained for the modified Kratzer and the corrected Morse potentials with the position-dependent effective mass. The bound state energy eigenvalues and the corresponding eigenfunctions are calculated for any angular momentum for target potentials. Various forms of point canonical transformations are applied.

Analytical solutions of fractional Schrödinger equation and thermal properties of Morse potential for some diatomic molecules

2021 ◽  
pp. 2150041
Author(s):  
U. S. Okorie ◽  
A. N. Ikot ◽  
G. J. Rampho ◽  
P. O. Amadi ◽  
Hewa Y. Abdullah
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Morse Potential ◽  
State Energy ◽  
Diatomic Molecules ◽  
Bound State ◽  
Bound State Energy ◽  
Fractional Schrödinger Equation ◽  
Energy Eigenvalues ◽  
Fractional Schrodinger Equation

By employing the concept of conformable fractional Nikiforov–Uvarov (NU) method, we solved the fractional Schrödinger equation with the Morse potential in one dimension. The analytical expressions of the bound state energy eigenvalues and eigenfunctions for the Morse potential were obtained. Numerical results for the energies of Morse potential for the selected diatomic molecules were computed for different fractional parameters chosen arbitrarily. Also, the graphical variation of the bound state energy eigenvalues of the Morse potential for hydrogen dimer with vibrational quantum number and the range of the potential were discussed, with regards to the selected fractional parameters. The vibrational partition function and other thermodynamic properties such as vibrational internal energy, vibrational free energy, vibrational entropy and vibrational specific heat capacity were evaluated in terms of temperature. Our results are new and have not been reported in any literature before.

scholarly journals Surface interaction effects to a Klein–Gordon particle embedded in a Woods–Saxon potential well in terms of thermodynamic functions,

2018 ◽  
Vol 96 (7) ◽  
pp. 843-850 ◽  
Author(s):  
B.C. Lütfüoğlu
Keyword(s):  
Thermodynamic Functions ◽  
State Energy ◽  
Gordon Equation ◽  
Surface Effect ◽  
Bound State ◽  
Point Of View ◽  
Potential Well ◽  
Saxon Potential ◽  
Relativistic Regime ◽  
Klein Gordon

Recently, it has been investigated how the thermodynamic functions vary when the surface interactions are taken into account for a nucleon that is confined in a Woods–Saxon potential well, with a non-relativistic point of view. In this manuscript, the same problem is handled with a relativistic point of view. More precisely, the Klein–Gordon equation is solved in the presence of mixed scalar–vector generalized symmetric Woods–Saxon potential energy that is coupled to momentum and mass. Employing the continuity conditions the bound state energy spectra of an arbitrarily parameterized well are derived. It is observed that, when a term representing the surface effect is taken into account, the character of Helmholtz free energy and entropy versus temperature are modified in a similar fashion as this inclusion is done in the non-relativistic regime. Whereas it is found that this inclusion leads to different characters to internal energy and specific heat functions for relativistic and non-relativistic regimes.

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