scholarly journals Analytical Bound State Solutions of the Klein-Fock-Gordon Equation for the Sum of Hulthén and Yukawa Potential within SUSY Quantum Mechanics

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
A. I. Ahmadov ◽  
S. M. Aslanova ◽  
M. Sh. Orujova ◽  
S. V. Badalov
Keyword(s):  
Quantum Mechanics ◽  
Gordon Equation ◽  
Jacobi Polynomials ◽  
Yukawa Potential ◽  
Scalar Potential ◽  
Bound State ◽  
Wave Functions ◽  
Relativistic Energy ◽  
Radial Wave ◽  
Energy Eigenvalues

The relativistic wave equations determine the dynamics of quantum fields in the context of quantum field theory. One of the conventional tools for dealing with the relativistic bound state problem is the Klein-Fock-Gordon equation. In this work, using a developed scheme, we present how to surmount the centrifugal part and solve the modified Klein-Fock-Gordon equation for the linear combination of Hulthén and Yukawa potentials. In particular, we show that the relativistic energy eigenvalues and corresponding radial wave functions are obtained from supersymmetric quantum mechanics by applying the shape invariance concept. Here, both scalar potential conditions, which are whether equal and nonequal to vector potential, are considered in the calculation. The energy levels and corresponding normalized eigenfunctions are represented as a recursion relation regarding the Jacobi polynomials for arbitrary l states. Beyond that, a closed form of the normalization constant of the wave functions is found. Furthermore, we state that the energy eigenvalues are quite sensitive with potential parameters for the quantum states. The nonrelativistic and relativistic results obtained within SUSY QM overlap entirely with the results obtained by ordinary quantum mechanics, and it displays that the mathematical implementation of SUSY quantum mechanics is quite perfect.

scholarly journals Bound state solution of the Klein–Fock–Gordon equation with the Hulthén plus a ring-shaped-like potential within SUSY quantum mechanics

2018 ◽  
Vol 33 (33) ◽  
pp. 1850203 ◽  
Author(s):  
A. I. Ahmadov ◽  
Sh. M. Nagiyev ◽  
M. V. Qocayeva ◽  
K. Uzun ◽  
V. A. Tarverdiyeva
Keyword(s):  
Quantum Mechanics ◽  
Gordon Equation ◽  
Jacobi Polynomials ◽  
Scalar Potential ◽  
Bound State ◽  
Wave Functions ◽  
State Solution ◽  
Bound State Solution ◽  
Radial Wave ◽  
Energy Eigenvalues

In this paper, the bound state solution of the modified Klein–Fock–Gordon equation is obtained for the Hulthén plus ring-shaped-like potential by using the developed scheme to overcome the centrifugal part. The energy eigenvalues and corresponding radial and azimuthal wave functions are defined for any [Formula: see text] angular momentum case on the conditions that scalar potential is whether equal and nonequal to vector potential, the bound state solutions of the Klein–Fock–Gordon equation of the Hulthén plus ring-shaped-like potential are obtained by Nikiforov–Uvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. The equivalent expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformations to each other is revealed owing to both methods. The energy levels and the corresponding normalized eigenfunctions are represented in terms of the Jacobi polynomials for arbitrary [Formula: see text] states. A closed form of the normalization constant of the wave functions is also found. It is shown that the energy eigenvalues and eigenfunctions are sensitive to [Formula: see text] radial and [Formula: see text] orbital quantum numbers.

Analytical bound-state solutions of the Schrödinger equation for the Manning–Rosen plus Hulthén potential within SUSY quantum mechanics

2018 ◽  
Vol 33 (03) ◽  
pp. 1850021 ◽  
Author(s):  
A. I. Ahmadov ◽  
Maria Naeem ◽  
M. V. Qocayeva ◽  
V. A. Tarverdiyeva
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Jacobi Polynomials ◽  
Bound State ◽  
Wave Functions ◽  
Hulthén Potential ◽  
Radial Wave ◽  
Energy Eigenvalues ◽  
Hulthen Potential

In this paper, the bound-state solution of the modified radial Schrödinger equation is obtained for the Manning–Rosen plus Hulthén potential by using new developed scheme to overcome the centrifugal part. The energy eigenvalues and corresponding radial wave functions are defined for any [Formula: see text] angular momentum case via the Nikiforov–Uvarov (NU) and supersymmetric quantum mechanics (SUSY QM) methods. Thanks to both methods, equivalent expressions are obtained for the energy eigenvalues, and the expression of radial wave functions transformations to each other is presented. The energy levels and the corresponding normalized eigenfunctions are represented in terms of the Jacobi polynomials for arbitrary [Formula: see text] states. A closed form of the normalization constant of the wave functions is also found. It is shown that, the energy eigenvalues and eigenfunctions are sensitive to [Formula: see text] radial and [Formula: see text] orbital quantum numbers.

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.

Relativistic quantum motion of spin-0 particles with a Cornell-type potential in (1 + 2)-dimensional Gürses spacetime backgrounds

2019 ◽  
Vol 34 (38) ◽  
pp. 1950314 ◽  
Author(s):  
Faizuddin Ahmed
Keyword(s):  
Quantum Dynamics ◽  
Gordon Equation ◽  
Relativistic Quantum ◽  
Scalar Potential ◽  
Wave Functions ◽  
Energy Eigenvalues ◽  
Klein Gordon ◽  
Quantum Motion ◽  
Type Potential ◽  
Klein Gordon Equation

In this work, we investigate the relativistic quantum dynamics of spin-0 particles in the background of (1 + 2)-dimensional Gürses spacetime [M. Gürses, Class. Quantum Grav. 11, 2585 (1994)] with interactions. We solve the Klein–Gordon equation subject to Cornell-type scalar potential in the considered framework, and evaluate the energy eigenvalues and corresponding wave functions, in detail.

scholarly journals Energy Eigenvalues and Eigenfunctions of a Diatomic Molecule in Quadratic Exponential-type Potential

2020 ◽  
Vol 3 (2) ◽  
pp. 240-251
Author(s):  
ES Eyube ◽  
U Wadata ◽  
SD Najoji
Keyword(s):  
Exponential Type ◽  
State Energy ◽  
Bound State ◽  
Wave Functions ◽  
Closed Form Expression ◽  
Bound State Energy ◽  
Form Expression ◽  
Radial Wave ◽  
Energy Eigenvalues ◽  
Type Potential

We have employed the exact quantization rule to obtain closed form expression for the bound state energy eigenvalues of a molecule in quadratic exponential-type potential. To deal with the spin-orbit centrifugal term of the effective potential energy function, we have used a Pekeris-type approximation scheme, we have also obtained closed form expression for the normalized radial wave functions by solving the Riccati equation with quadratic exponential-type potential. Using our derived energy eigenvalue formula, we have deduced expressions for the bound state energy eigenvalues of the Hulthén, Eckart and Deng-Fan potentials, considered as special cases of the quadratic exponential-type potential. Our deduced energy eigenvalues are in excellent agreement with those in the literature. We have computed bound states energy eigenvalues for six diatomic molecules viz: HCl, LiH, H2, SeH, VH and TiH. Our results are in total agreement with existing results in the literature for the s-wave and in good agreement for higher quantum states. By solving the Riccati equation, we have obtained normalized radial wave functions of the quadratic exponential-type potential, our results show higher probabilities of finding the molecule in the region 0.1 ≤ y ≤ 0.2

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.

scholarly journals APPROXIMATE ℓ-STATE SOLUTION OF TIME INDEPENDENT SCHRÖDINGER WAVE EQUATION WITH MODIFIED MÖBIUS SQUARED POTENTIAL PLUS HULTHÉN POTENTIAL

2020 ◽  
Vol 4 (2) ◽  
pp. 425-435
Author(s):  
Dlama Yabwa ◽  
Eyube E.S ◽  
Yusuf Ibrahim
Keyword(s):  
State Energy ◽  
Approximation Scheme ◽  
Bound State ◽  
Wave Functions ◽  
Bound State Energy ◽  
Hulthén Potential ◽  
Radial Wave ◽  
Energy Eigenvalues ◽  
Type Approximation ◽  
Hulthen Potential

In this work we have applied ansatz method to solve for the approximate ℓ-state solution of time independent Schrödinger wave equation with modified Möbius squared potential plus Hulthén potential to obtain closed form expressions for the energy eigenvalues and normalized radial wave-functions. In dealing with the spin-orbit coupling potential of the effective potential energy function, we have employed the Pekeris type approximation scheme, using our expressions for the bound state energy eigenvalues, we have deduced closed form expressions for the bound states energy eigenvalues and normalized radial wave-functions for Hulthén potential, modified Möbius square potential and Deng-Fan potential. Using the value 0.976865485225 for the parameter ω, we have computed bound state energy eigenvalues for various quantum states (in atomic units). We have also computed bound state energy eigenvalues for six diatomic molecules: HCl, LiH, TiH, NiC, TiC and ScF. The results we obtained are in near perfect agreement with numerical results in the literature and a clear demonstration of the superiority of the Pekeris-type approximation scheme over the Greene and Aldrich approximation scheme for the modified Möbius squares potential plus Hulthén potential.

A new theoretical study of the deformed unequal scalar and vector Hellmann plus modified Kratzer potentials within the deformed Klein–Gordon equation in RNCQM symmetries

2021 ◽  
Author(s):  
Abdelmadjid Maireche
Keyword(s):  
Quantum Mechanics ◽  
Yukawa Potential ◽  
Relativistic Quantum ◽  
Scalar Potential ◽  
Relativistic Quantum Mechanics ◽  
Energy Eigenvalues ◽  
Quantum Numbers ◽  
Noncommutative Quantum Mechanics ◽  
Hellmann Potential ◽  
Klein Gordon

In this paper, within the framework of relativistic quantum mechanics and using the improved approximation scheme to the centrifugal term for any [Formula: see text]states via Bopp’s shift method and standard perturbation theory, we have obtained the modified energy eigenvalues of a newly proposed modified unequal vector and scalar Hellmann plus modified Kratzer potentials (DUVSHMK-Ps) for some diatomic N2, I2, CO, NO, O2 and HCl molecules. This study includes corrections of the first-order in noncommutativity parameters [Formula: see text]. This potential is a superposition of the attractive Coulomb Yukawa potential plus the Kratzer potential and new central terms appear as a result of the effects of noncommutativity properties of space–space. The obtained energy eigenvalues appear as a function of noncommutativity parameters, the strength parameters [Formula: see text] and [Formula: see text] of the (scalar vector) Hellmann potential, the screening range parameter [Formula: see text], the dissociation energy of the vector, and scalar potential [Formula: see text], the equilibrium inter-nuclear distance [Formula: see text] in addition to the atomic quantum numbers [Formula: see text]. Furthermore, we obtained the corresponding modified energy of DUVSHMK-Ps in the symmetries of non-relativistic noncommutative quantum mechanics (NRNCQM). In both relativistic and non-relativistic problems, we show that the corrections on the spectrum energy are smaller than the main energy in the ordinary cases of RQM and NRQM.

scholarly journals Bound states of the D-dimensional Schrödinger equation for the generalized Woods–Saxon potential

2019 ◽  
Vol 34 (14) ◽  
pp. 1950107 ◽  
Author(s):  
V. H. Badalov ◽  
B. Baris ◽  
K. Uzun
Keyword(s):  
Quantum Mechanics ◽  
Energy Spectrum ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Wave Functions ◽  
Basis Set ◽  
Saxon Potential ◽  
Radial Wave ◽  
Energy Eigenvalues ◽  
Approximate Analytical Solutions

The formal framework for quantum mechanics is an infinite number of dimensional space. Hereby, in any analytical calculation of the quantum system, the energy eigenvalues and corresponding wave functions can be represented easily in a finite-dimensional basis set. In this work, the approximate analytical solutions of the hyper-radial Schrödinger equation are obtained for the generalized Wood–Saxon potential by implementing the Pekeris approximation to surmount the centrifugal term. The energy eigenvalues and corresponding hyper-radial wave functions are derived for any angular momentum case by means of state-of-the-art Nikiforov–Uvarov and supersymmetric quantum mechanics methods. Hence, the same expressions are obtained for the energy eigenvalues, and the expression of hyper-radial wave functions transforming each other is shown owing to these methods. Furthermore, a finite number energy spectrum depending on the depths of the potential well [Formula: see text] and [Formula: see text], the radial [Formula: see text] and [Formula: see text] orbital quantum numbers and parameters [Formula: see text], [Formula: see text], [Formula: see text] are also identified in detail. Next, the bound state energies and corresponding normalized hyper-radial wave functions for the neutron system of the [Formula: see text]Fe nucleus are calculated in [Formula: see text] and [Formula: see text] as well as the energy spectrum expressions of other higher dimensions are revealed by using the energy spectrum of [Formula: see text] and [Formula: see text].

scholarly journals BOUND STATES OF THE KLEIN–GORDON EQUATION FOR VECTOR AND SCALAR GENERAL HULTHÉN-TYPE POTENTIALS IN D-DIMENSION

2009 ◽  
Vol 20 (01) ◽  
pp. 25-45 ◽  
Author(s):  
SAMEER M. IKHDAIR
Keyword(s):  
Bound States ◽  
Gordon Equation ◽  
Jacobi Polynomials ◽  
Rest Mass ◽  
Bound State ◽  
Binding Energies ◽  
S Wave ◽  
Energy Eigenvalues ◽  
Klein Gordon ◽  
Klein Gordon Equation

We solve the Klein–Gordon equation in any D-dimension for the scalar and vector general Hulthén-type potentials with any l by using an approximation scheme for the centrifugal potential. Nikiforov–Uvarov method is used in the calculations. We obtain the bound-state energy eigenvalues and the corresponding eigenfunctions of spin-zero particles in terms of Jacobi polynomials. The eigenfunctions are physical and the energy eigenvalues are in good agreement with those results obtained by other methods for D = 1 and 3 dimensions. Our results are valid for q = 1 value when l ≠ 0 and for any q value when l = 0 and D = 1 or 3. The s-wave (l = 0) binding energies for a particle of rest mass m0 = 1 are calculated for the three lower-lying states (n = 0, 1, 2) using pure vector and pure scalar potentials.

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