Non-central Potential Research Articles

Asymptotic iteration method for the modified Pöschl–Teller potential and trigonometric Scarf II non-central potential in the Dirac equation spin symmetry

Analytical solution of the Dirac equation for the modified Poschl–Teller potential and trigonometric Scarf II non-central potential for spin symmetry is studied using asymptotic iteration method. One-dimensional Dirac equation consisting of the radial and angular parts can be obtained by the separation of variables. By using asymptotic iteration method, the relativistic energy equation and orbital quantum number (l) equation can be obtained, where both are interrelated. Relativistic energy equation is calculated numerically by the Matlab software. The increase in the radial quantum number n r causes a decrease in the energy value, and the wave functions of the radial and the angular parts are expressed in terms of hypergeometric functions. Some thermodynamical properties of the system can be determined by reducing the relativistic energy equation to the non-relativistic energy equation. Thermodynamical properties such as vibrational partition function, vibrational specific heat function and vibrational mean energy function are expressed in terms of error function.

Scattering states of the Schrödinger equation with a position-dependent-mass and a non-central potential

In this paper, we study the time-independent Schr¨odinger equation within the formalism of a position-dependent effective mass. By using a generalized decomposition of a non-central effective potential, The deformed Schr¨odinger equation can be easily solved analytically through separation of variables. The energy eigenvalues and the normalization constant of the radial wave functions, as well as the scattering phase shifts are obtained.

Energy analysis of four dimensional extended hyperbolic Scarf I plus three dimensional separable trigonometric noncentral potentials using SUSY QM approach

The non-relativistic energies and wave functions of extended hyperbolic Scarf I plus separable non-central shape invariant potential in four dimensions are investigated using Supersymmetric Quantum Mechanics (SUSY QM) Approach. The three dimensional separable non-central shape invariant angular potential consists of trigonometric Scarf II, Manning Rosen and Poschl-Teller potentials. The four dimensional Schrodinger equation with separable shape invariant non-central potential is reduced into four one dimensional Schrodinger equations through variable separation method. By using SUSY QM, the non-relativistic energies and radial wave functions are obtained from radial Schrodinger equation, the orbital quantum numbers and angular wave functions are obtained from angular Schrodinger equations. The extended potential means there is perturbation terms in potential and cause the decrease in energy spectra of Scarf I potential.

Supersymmetric approach for Killingbeck radial potential plus noncentral potential in Schrodinger equation

Killingbeck radial potential, which consists of harmonic oscillator, linier and Coulomb potentials, is combined with non-central potential. The solution of three dimensional Schrodinger equation for Killingbeck potential is combined with Poschl-Teller potential and Symmetrical Top non-central potentials are investigated using supersymmetry (SUSY) operator. The non-relativistic energy is obtained which is infuenced by potentials and the wave functions are produced by using SUSY operator.

Analysis of D Dimensional Dirac equation for q-deformed Posch-Teller combined with q-deformed trigonometric Manning Rosen Non-Central potential using Asymptotic Iteration Method (AIM)

In this study, we used asymptotic iteration method (AIM) to obtain the relativistic energy spectra and wavefunctions for D Dimensional Dirac equation. Solution of the D Dimensional Dirac equation using asymptotic iteration method was done by four steps. The first step, we substitutied q deformed Poschl-Teller potential plus q-deformed Manning Rosen Non-Central potential into D dimensional Dirac equation. And then, general term of D dimensioanl Dirac equation for q deformed Poschl-Teller potential plus q-deformed Manning Rosen Non-Central potential was reduced into one dimensioanal Dirac equation, consist of radial part and angular part. The second step, both of one dimensional part must be reduced to hypergeometric type differential equation by suitable parameter change. And then, hypergeometric type differential equation was transformed into AIM type differential equation. For the last step, AIM type differential equation can be solved to obtain the relativistic energy and wavefunctions of Dirac equation. Relativistic energy and wavefunctions were visualized by using Matlab software.

Solution of three dimensional Schrodinger equation for Eckart and Manning-Rosen non-central potential using asymptotic iteration method

Solution of Schrodinger equation in three dimensions for Eckart and Manning-Rosen potential has been obtained by using the asymptotic iteration method. Energy spectrum and wave function for these potentials was obtained. It is known that the wave function for the corresponding potentials contains hypergeometric series due to the type of Schrodinger equation. However, the wave function for radial part is not normalizable, due to its equation that reaches to infinity when r equals to zero. The energy spectrum and wave function for corresponding potentials had also been analyzed with the help of Matlab R2013a software.

Quantum mechanical treatment of a constrained particle on two dimensional sphere

In this work, we study the motion of a particle on two dimensional sphere. By writing the Schrodinger equation, we obtain the wave function and energy spectra for three dimensional harmonic oscillator potential plus trigonometric Rosen–Morse non-central potential. By letting three special cases for intertwining operator, we investigate the energy spectra and wave functions for Smorodinsky–Winternitz potential model.

Analytical solutions for a double ring-shaped noncentral potential in D-dimensions

In the present study, a generalized double ring-shaped Coulomb noncentral potential is proposed, and the D-dimensional Schrodinger equation with this potential is examined in hyperspherical coordinates. The Nikiforov-Uvarov (N-U) method is applied to obtain the D-dimensional energy eigenvalues and the corresponding eigenfunctions. The angular/radial wavefunction is written in terms of Jacobi/Laguerre polynomials.

Quantization of time-dependent singular potential systems: Non-central potential in three dimensions

Quantum features of a dynamical system subjected to time-dependent non-central potentials are investigated. The entire potential of the system is composed of the inverse quadratic potential and the Coulomb potential. An invariant operator that enables us to treat the time-dependent Hamiltonian system in view of quantum mechanics is introduced in order to derive Schrödinger solutions (wave functions) of the system. To simplify the problem, the invariant operator is transformed to a simple form by unitary transformation. Quantum solutions in the transformed system are easily obtained because the transformed invariant operator is a time-independent simple one. The Nikiforov-Uvarov method is used for solving eigenvalue equation of the transformed invariant operator. The double ring-shaped generalized non-central time-dependent potential is considered as a particular case for further study. From inverse transformation of quantum solutions obtained in the transformed system, the complete quantum solutions in the original system are identified. The quantum properties of the system are addressed on the basis of the wave functions.

Uniform asymptotic approximation for 3D quantum scattering by a non-central potential

An Ansatz based on an etalon function generated by the problem itself is used in order to obtain a uniform asymptotic approximation of the 3D wave function for the scattering by a non-central potential. The obtained uniform asymptotic approximation removes the singularities at the caustics that occur in the 3D WKB approximation. The scattering amplitude provided by the uniform asymptotic approximation contains the poles that are the fingerprints of the system. The comparison of the obtained uniform asymptotic approximation of the 3D scattering wave function with the exact scattering wave function shows the versatility of the Ansatz based on an etalon function generated by the problem itself.

Schrödinger equation with a non-central potential: Some statistical quantities

In this paper, we study the dependence of some statistical quantities such as the free energy, the mean energy, the entropy, and the specific heat for the Schrodinger equation on the temperature, particularly in the case of a non-central potential. The basic point is to find the partition function which is obtained by a method based on the Euler-Maclaurin formula. At first, we present the analytical results supporting them with some plots for the thermal functions for one- and three-dimensional cases to find out the effect of the angular momentum. We also study then the effect of the angle-dependent part of the non-central potential. We discuss the results briefly for a phase transition for the system. We also present our results for a three-dimesional harmonic oscillator.

Approximate analytical solution of the Dirac equation for pseudospin symmetry with modified Po schl-Teller potential and trigonometric Scarf II non-central potential using asymptotic iteration method

We apllied asymptotic iteration method (AIM) to obtain the analytical solution of the Dirac equation in case exact pseudospin symmetry in the presence of modified Pcischl- Teller potential and trigonometric Scarf II non-central potential. The Dirac equation was solved by variables separation into one dimensional Dirac equation, the radial part and angular part equation. The radial and angular part equation can be reduced into hypergeometric type equation by variable substitution and wavefunction substitution and then transform it into AIM type equation to obtain relativistic energy eigenvalue and wavefunctions. Relativistic energy was calculated numerically by Matlab software. And then relativistic energy spectrum and wavefunctions were visualized by Matlab software. The results show that the increase in the radial quantum number nr causes decrease in the relativistic energy spectrum. The negative value of energy is taken due to the pseudospin symmetry limit. Several quantum wavefunctions were presented in terms of the hypergeometric functions.

Solusi Persamaan Schrödinger untuk Potensial Hulthen + Non-Sentral Poschl-Teller dengan Menggunakan Metode Nikiforov-Uvarov

<span>The Schrödinger equation for Hulthen potential plus Poschl-Teller Non-Central potential is <span>solved analytically using Nikiforov-Uvarov method. The radial equation and angular equation <span>are obtained through the variable separation. The solving of Schrödinger equation with <span>Nikivorov-Uvarov method (NU) has been done by reducing the two order differensial equation <span>to be the two order differential equation Hypergeometric type through substitution of <span>appropriate variables. The energy levels obtained is a closed function while the wave functions <span>(radial and angular part) are expressed in the form of Jacobi polynomials. The Poschl-Teller <span>Non-Central potential causes the orbital quantum number increased and the energy of the <span>Hulthen potential is increasing positively.</span></span></span></span></span></span></span></span><br /></span>

Solution of The Schrödinger Equation for Trigonometric Scarf Plus Poschl-Teller Non-Central Potential Using Supersymmetry Quantum Mechanics

<span>In this paper, we show that the exact energy eigenvalues and eigen functions of the Schrödinger <span>equation for charged particles moving in certain class of noncentral potentials can be easily <span>calculated analytically in a simple and elegant manner by using Supersymmetric method <span>(SUSYQM). We discuss the trigonometric Scarf plus Poschl-Teller systems. Then, by operating <span>the lowering operator we get the ground state wave function, and the excited state wave functions <span>are obtained by operating raising operator repeatedly. The energy eigenvalue is expressed in the <span>closed form obtained using the shape invariant properties. The results are in exact agreement with <span>other methods.</span></span></span></span></span></span></span><br /></span>

Thermodynamics properties study of diatomic molecules with q-deformed modified Poschl-Teller plus Manning Rosen non-central potential in D dimensions using SUSYQM approach

D-dimensional Dirac equation of q-deformed modified Poschl-Teller plus Manning Rosen non-central potential was solved using supersymmetric quantum mechanics (SUSY QM). The relativistic energy spectra were analyzed by using SUSY QM and shape invariant properties from radial part of D dimensional Dirac equation and the angular quantum numbers were obtained from angular part of D dimensional Dirac equation. The SUSY operators was used to generate the D dimensional relativistic wave functions both for radial and angular parts. In the non-relativistic limit, the relativistic energy equation was reduced to the non-relativistic energy. In the classical limit, the partition function of vibrational, the specific heat of vibrational, and the mean energy of vibrational of some diatomic molecules were calculated from the equation of non-relativistic energy with the help of error function and Mat-lab 2011.

Simple way to extract solutions and features of the Dirac equation for a noncentral potentials

The main purpose of the present study is to explore the classes of the Schrödinger-like wave equations derived from Dirac equation, for which the similarity transformation and asymptotic iteration algorithms can assist in generating second-order differential equation that admit general exact solutions in the presence of nonsymmetrical potential terms. For illustration purposes, we extract the exact bound-state solutions of the Dirac equation with the noncentral Hartmann potential for the cases of exact [Formula: see text] spin and pseudospin symmetries. Also, we have shown that both Dirac-radial and Dirac-polar parts are sensitive to the variation of the involved parameters.

Non-central potentials in the cosmic string space–time

We investigate the behavior of quantum particles in the cosmic string space–time in the presence of Pöschl–Teller double-ring-shaped Coulomb and double-ring-shaped oscillator potentials. We obtain energy levels and finally compare the results with the Minkowski space–time. To do this, we solve the Schrödinger equation in spherical coordinates.

Relativistic Energy Analysis of Five-Dimensionalq-Deformed Radial Rosen-Morse Potential Combined withq-Deformed Trigonometric Scarf Noncentral Potential Using Asymptotic Iteration Method

We study the exact solution of Dirac equation in the hyperspherical coordinate under influence of separableq-deformed quantum potentials. Theq-deformed hyperbolic Rosen-Morse potential is perturbed byq-deformed noncentral trigonometric Scarf potentials, where all of them can be solved by using Asymptotic Iteration Method (AIM). This work is limited to spin symmetry case. The relativistic energy equation and orbital quantum number equationlD-1have been obtained using Asymptotic Iteration Method. The upper radial wave function equations and angular wave function equations are also obtained by using this method. The relativistic energy levels are numerically calculated using Matlab, and the increase of radial quantum numberncauses the increase of bound state relativistic energy level in both dimensionsD=5andD=3. The bound state relativistic energy level decreases with increasing of both deformation parameterqand orbital quantum numbernl.

A uniform asymptotic approximation of the 3D scattering wave function for a non-central Coulomb-like potential

A uniform asymptotic approximation of the 3D scattering wave function for a non-central Coulomb-like potential is obtained. It is based on a new Ansatz of the form of the solution that uses an etalon function generated by the problem itself, rather than a special function. First the 3D WKB approximation of the scattering wave function for the non-central Coulomb-like potential is obtained. This approximation is valid on the whole range of the variables, except for the caustics. The uniform approximation eliminates the shortcoming of the 3D WKB approximation, being valid on the whole range of the variables, including the caustics. The scattering amplitude for the non-central Coulomb-like potential is obtained.

On Solving the Schrödinger Equation for Three-Dimensional Noncentral Potential

On Solving the Schrödinger Equation for Three-Dimensional Noncentral Potential