ARBITRARY ℓ-STATE SOLUTION OF THE HELLMANN 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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ACCURATE ITERATIVE AND PERTURBATIVE SOLUTIONS OF THE YUKAWA POTENTIAL

International Journal of Modern Physics E ◽

10.1142/s0218301306004806 ◽

2006 ◽

Vol 15 (06) ◽

pp. 1253-1262 ◽

Cited By ~ 18

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.

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Bound state energy eigenvalues of generalized Hellmann potential

Physica Scripta ◽

10.1088/0031-8949/51/1/002 ◽

1995 ◽

Vol 51 (1) ◽

pp. 13-15 ◽

Cited By ~ 4

Author(s):

Ramazan Sever ◽

Cevdet Tezcan

Keyword(s):

State Energy ◽

Bound State ◽

Bound State Energy ◽

Energy Eigenvalues ◽

Hellmann Potential

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

Open Physics ◽

10.2478/s11534-012-0018-y ◽

2012 ◽

Vol 10 (4) ◽

Cited By ~ 7

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.

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

International Journal of Modern Physics E ◽

10.1142/s0218301308010428 ◽

2008 ◽

Vol 17 (07) ◽

pp. 1327-1334 ◽

Cited By ~ 22

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.

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

Modern Physics Letters A ◽

10.1142/s0217732321500413 ◽

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.

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Bound state energy eigenvalues for a general class of one‐dimensional problems on the whole axis (−∞, ∞) via the Prüfer transformation

Journal of Mathematical Physics ◽

10.1063/1.526119 ◽

1984 ◽

Vol 25 (12) ◽

pp. 3497-3502

Author(s):

I. Úlehla ◽

D. Adamová

Keyword(s):

General Class ◽

State Energy ◽

Bound State ◽

Bound State Energy ◽

One Dimensional ◽

Energy Eigenvalues

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Analytical solution of energy eigen value, eigen function and angular wave function of Dirac equation with Rosen Morse plus Rosen Morse potential in terms of Romanovski polynomials for exact spin symmetry

Journal of Physics Theories and Applications ◽

10.20961/jphystheor-appl.v1i1.4700 ◽

2017 ◽

Vol 1 (1) ◽

pp. 1

Author(s):

Ihtiari Prasetyaningrum ◽

C Cari ◽

A Suparmi

Keyword(s):

Dirac Equation ◽

Morse Potential ◽

State Energy ◽

Spin Symmetry ◽

Bound State ◽

Bound State Energy ◽

Eigenvalues And Eigenfunctions ◽

Energy Eigenvalues ◽

Eigen Value ◽

Energy Eigenvalues And Eigenfunctions

<p class="Abstract">The energy eigenvalues and eigenfunctions of Dirac equation for Rosen Morse plus Rosen Morse potential are investigated numerically in terms of finite Romanovsky Polynomial. The bound state energy eigenvalues are given in a closed form and corresponding eigenfunctions are obtained in terms of Romanovski polynomials. The energi eigen value is solved by numerical method with Matlab 2011.</p>

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ENERGY SPECTRUM AND SOME USEFUL EXPECTATION VALUES OF THE TIETZ-HULTHÉN POTENTIAL

FUDMA Journal of Sciences ◽

10.33003/fjs-2021-0501-614 ◽

2021 ◽

Vol 5 (2) ◽

pp. 255-263

Author(s):

Bako M. Bitrus ◽

U Wadata ◽

C. M. Nwabueze ◽

E. S. Eyube

Keyword(s):

Kinetic Energy ◽

State Energy ◽

Bound State ◽

Solution Technique ◽

Bound State Energy ◽

Solid State Physics ◽

Expectation Values ◽

Hulthén Potential ◽

Energy Eigenvalues ◽

Hulthen Potential

In this paper, concept of supersymmetric quantum mechanics has been employed to derive expression for bound state energy eigenvalues of the Tietz-Hulthén potential, the corresponding equation for normalized radial eigenfunctions were deduced by ansatz solution technique. In dealing with the centrifugal term of the effective potential of the Schrödinger equation, a Pekeris-like approximation recipe is considered. By means of the expression for bound state energy eigenvalues and radial eigenfunctions, equations for expectation values of inverse separation-squared and kinetic energy of the Tietz-Hulthén potential were obtained from the Hellmann-Feynman theorem. Numerical values of bound state energy eigenvalues and expectation values of inverse separation-squared and kinetic energy the Tietz-Hulthén potential were computed at arbitrary principal and angular momentum quantum numbers. Results obtained for computed energy eigenvalues of Tietz-Hulthén potential corresponding to Z = 0 and V0 = 0 are in excellent agreement with available literature data for Tietz and Hulthén potentials respectively. Studies have also revealed that increase in parameter Z results in monotonic increase in the mean kinetic energy of the system. The results obtained in this work may find suitable applications in areas of physics such as: atomic physics, chemical physics, nuclear physics and solid state physics

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Analytical solution of energy eigen value, eigen function and angular wave function of Dirac equation with Rosen Morse plus Rosen Morse potential in terms of Romanovski polynomials for exact spin symmetry

Journal of Theoretical and Applied Physics ◽

10.20961/jotap.v1i1.4700 ◽

2017 ◽

Vol 1 (1) ◽

pp. 1

Author(s):

Ihtiari Prasetyaningrum ◽

C Cari ◽

A Suparmi

Keyword(s):

Dirac Equation ◽

Morse Potential ◽

State Energy ◽

Spin Symmetry ◽

Bound State ◽

Bound State Energy ◽

Eigenvalues And Eigenfunctions ◽

Energy Eigenvalues ◽

Eigen Value ◽

Energy Eigenvalues And Eigenfunctions

<p class="Abstract">The energy eigenvalues and eigenfunctions of Dirac equation for Rosen Morse plus Rosen Morse potential are investigated numerically in terms of finite Romanovsky Polynomial. The bound state energy eigenvalues are given in a closed form and corresponding eigenfunctions are obtained in terms of Romanovski polynomials. The energi eigen value is solved by numerical method with Matlab 2011.</p>

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