ACCURATE ITERATIVE AND PERTURBATIVE SOLUTIONS OF THE YUKAWA POTENTIAL

2006 ◽  
Vol 15 (06) ◽  
pp. 1253-1262 ◽  
Author(s):  
M. KARAKOC ◽  
I. BOZTOSUN
Keyword(s):  
Numerical Methods ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
State Energy ◽  
Yukawa Potential ◽  
Bound State ◽  
Asymptotic Iteration Method ◽  
Bound State Energy ◽  
Energy Eigenvalues ◽  
Radial Schrödinger Equation

We apply the asymptotic iteration method to solve the radial Schrödinger equation for the Yukawa type potentials. The solution of the radial Schrödinger equation by using different approaches requires tedious and cumbersome calculations; however, we present that it is possible to obtain the bound state energy eigenvalues for any n and ℓ values easily within the framework of this method. We also show the perturbed application of this method for the same potential. Our results are in excellent agreement with the findings of the SUSY perturbation, 1/N expansion and numerical methods.

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 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.

Solutions of Schrodinger equation and thermodynamic properties of Iodine and Scandium Fluoride molecules based on Formula method

2021 ◽  
Author(s):  
Ifeanyi Jude Njoku ◽  
Chibueze Paul Onyenegecha ◽  
Chioma J Okereke ◽  
Ekwevugbe Omugbe ◽  
Emeka Onyeocha
Keyword(s):  
Partition Function ◽  
Thermodynamic Properties ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
State Energy ◽  
Bound State ◽  
Energy Solution ◽  
Bound State Energy ◽  
Radial Schrödinger Equation ◽  
Formula Method

Abstract The study presents the thermodynamic properties of the Iodine and Scandium Flouride molecules with molecular Deng-Fan potential. The bound state energy solution of the radial Schrodinger equation is obtained via the formula method. The partition function and other thermodynamic properties are evaluated via the Poisson summation approach. The numerical values of energy of the I2 and ScF molecules are found to be in agreement with results obtained from other methods in the literature. The results further show that the partition function decreases, and then converges to a constant value as temperature increases.

scholarly journals Solutions of Schrodinger Equation And Thermodynamic Properties of Potassium Dimer Based On Formular Method

2021 ◽  
Author(s):  
C. P. Onyenegecha ◽  
E. N. Omoko ◽  
I. J. Njoku ◽  
E. E. Oguzie ◽  
C. J. Okereke
Keyword(s):  
Partition Function ◽  
Thermodynamic Properties ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
State Energy ◽  
Bound State ◽  
Bound State Energy ◽  
Radial Schrödinger Equation ◽  
Potassium Dimer ◽  
Formula Method

Abstract The study presents the thermodynamic properties of the XI Σ+g state of potassium (K2) dimer with molecular Deng-Fan potential. The bound state energy solution of the radial Schrodinger equation is obtained via the formula method. The partition function and other thermodynamic properties are evaluated. The numerical values of energy are found to be in agreement with results obtained from other methods in literature. The results further show that the partition function increases as temperature decreases, which implies a decrease in the probability of finding a particle in a state with quantum number, n.

ARBITRARY ℓ-STATE SOLUTION OF THE HELLMANN POTENTIAL

2007 ◽  
Vol 06 (04) ◽  
pp. 893-903 ◽  
Author(s):  
G. KOCAK ◽  
O. BAYRAK ◽  
I. BOZTOSUN
Keyword(s):  
Iteration Method ◽  
State Energy ◽  
Bound State ◽  
Accurate Solution ◽  
State Solution ◽  
Asymptotic Iteration Method ◽  
Bound State Energy ◽  
Energy Eigenvalues ◽  
Radial Schrödinger Equation ◽  
Hellmann Potential

We present an alternative and accurate solution of the radial Schrödinger equation for the Hellmann potential within the framework of the asymptotic iteration method. We show that the bound state energy eigenvalues can be obtained easily for any n and ℓ values without using any approximations required by other methods. Our results are compared with the findings of other methods.

scholarly journals The bound state solutions of the D-dimensional Schrödinger equation for the Woods–Saxon potential

2016 ◽  
Vol 25 (01) ◽  
pp. 1650002 ◽  
Author(s):  
V. H. Badalov
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Bound State ◽  
Wave Functions ◽  
Saxon Potential ◽  
Radial Wave ◽  
Energy Eigenvalues ◽  
Quantum Numbers ◽  
Radial Schrödinger Equation ◽  
Pekeris Approximation

In this work, the analytical solutions of the [Formula: see text]-dimensional radial Schrödinger equation are studied in great detail for the Wood–Saxon potential by taking advantage of the Pekeris approximation. Within a novel improved scheme to surmount centrifugal term, the energy eigenvalues and corresponding radial wave functions are found for any angular momentum case within the context of the Nikiforov–Uvarov (NU) and Supersymmetric quantum mechanics (SUSYQM) methods. In this way, based on these methods, the same expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformed each other is demonstrated. In addition, a finite number energy spectrum depending on the depth of the potential [Formula: see text], the radial [Formula: see text] and orbital [Formula: see text] quantum numbers and parameters [Formula: see text] are defined as well.

scholarly journals Any l-State Solutions of the Schrodinger Equation for q-Deformed Hulthen Plus Generalized Inverse Quadratic Yukawa Potential in Arbitrary Dimensions

2019 ◽  
Vol 65 (4 Jul-Aug) ◽  
pp. 333 ◽  
Author(s):  
C. O. Edet ◽  
And P. O. Okoi
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Jacobi Polynomials ◽  
Generalized Inverse ◽  
Yukawa Potential ◽  
Bound State ◽  
Energy Eigenvalues ◽  
Special Cases ◽  
Different Dimensions ◽  
Arbitrary Dimensions

The bound state approximate solution of the Schrodinger equation is obtained for the q-deformed Hulthen plus generalized inverse quadratic Yukawa potential (HPGIQYP) in -dimensions using the Nikiforov-Uvarov (NU) method and the corresponding eigenfunctions are expressed in Jacobi polynomials. Seven special cases of the potential are discussed and the numerical energy eigenvalues are calculated for two values of the deformation parameter in different dimensions.

AN ALTERNATIVE ACCURATE SOLUTION OF THE EXPONENTIAL COSINE SCREENED COULOMB POTENTIAL

2007 ◽  
Vol 18 (09) ◽  
pp. 1443-1451 ◽  
Author(s):  
O. BAYRAK ◽  
I. BOZTOSUN
Keyword(s):  
Coulomb Potential ◽  
State Energy ◽  
Bound State ◽  
Accurate Solution ◽  
Asymptotic Iteration Method ◽  
Full Potential ◽  
Energy Eigenvalues ◽  
Screening Parameter ◽  
Radial Schrödinger Equation ◽  
Screened Coulomb Potential

In this paper, we show an alternative and accurate solution of the radial Schrödinger equation for the exponential cosine screened Coulomb potential within the framework of the asymptotic iteration method. Unlike other methods, which require approximations for the centrifugal or exponential terms, we show that it is possible to solve the full potential without making any approximations within the framework of this method. The bound state energy eigenvalues are obtained for any n and l values and the results are compared with the findings of different methods for several screening parameters. Moreover, we study the screening parameter δ = 0 case to obtain the energy eigenvalues and corresponding eigenfunctions of this potential in a closed-form.

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