Manning-Rosen Potential Research Articles

Exact Quantized Momentum Eigenvalues and Eigenstates of a General Potential Model

We obtain the quantized momentum eigenvalues, Pn, and the momentum eigenstates for the space-like Schr?dinger equation, the Feinberg-Horodecki equation, with the general potential which is constructed by the temporal counterpart of the spatial form of these potentials. The present work is illustrated with two special cases of the general form: time-dependent Wei-Hua Oscillator and time-dependent Manning-Rosen potential. We also plot the variations of the general molecular potential with its two special cases and their momentum states for few quantized states against the screening parameter.

Scattering with Manning–Rosen potential in all partial waves

Ordinary differential approach together with certain properties of Gaussian hypergeometric functions is exploited to construct exact analytical expressions for regular and irregular solutions in all partial waves for motion in Manning–Rosen potential. The Jost function thus obtained from the near the origin behaviour of the irregular solution is used appropriately to compute scattering phase shifts for the neutron–proton and neutron–deuteron systems for few lower partial waves. Our results are in good agreement with experimental data.

Bound state solutions of the Klein-Fock-Gordon equation with the sum of Manning-Rosen potential and Yukawa potential within SUSYQM

In this study, the bound state solutions of the Klein-Fock-Gordon equation are examined for the sum of Manning-Rosen and Yukawa potential by using a recent improved scheme to deal with the centrifugal term. For any l ≠ 0, the energy eigenvalues and corresponding radial wave functions are determined under the condition of equal scalar and vector potentials. In order to obtain bound state solutions, we use two different methods called supersymmetric quantum mechanics (SUSYQM) and Nikiforov-Uvarov (NU) methods. The identical expressions for the energy eigenvalues are obtained, and the expression of radial wave functions transformations to each other is revealed via both methods. For arbitrary l states, the energy levels and the corresponding normalized eigenfunctions are given in terms of the Jacobi polynomials. A closed form of the normalized wave function is also obtained. It is seen that the energy eigenvalues and eigenfunctions are sensitive to nr radial and l orbital quantum numbers.

Regular and Jost states for the S-wave Manning–Rosen potential

A regular solution for the Manning–Rosen potential is constructed by adapting the differential equation approach to the problem. The Jost solution and the Jost function are found by exploiting the relation between regular and irregular solutions. The Jost function thus obtained is applied for the first time to find bound state energies and the scattering phase shifts for nuclear systems.

Approximate solution of the Schrödinger equation with Manning-Rosen plus Hellmann potential and its thermodynamic properties using the proper quantization rule

We obtained, by using the proper quantization rule, the approximate solutions of the Schrodinger equation with Manning-Rosen plus Hellmann potential for any l-state. Furthermore, thermodynamic properties, such as the vibrational mean U , specific heat C, free energy F and entropy S for the pure vibrational state in the classical limit for these energy eigenvalues, are studied.

Analytical Solution of Dirac Equation for Hyperbolic Manning-Rosen-like Potential Using Hypergeometric Method for Exact Spin Symmetry

Analytical solution of Dirac equation for hyperbolic Manning-Rosen-like potential is obtained using hypergeometric method. The analytical solution is aimed to determine energy spectrum and radial wave function for this potential with exact spin symmetry. Behavior of atomic particles can be clearly understood if the energy spectrum and wave function of particle are known. Dirac equation for exact spin symmetry is reduced into a second order differential equation like Schrödinger equation. Hypergeometric method for Dirac equation with hyperbolic Manning-Rosen-like potential is the same as for Dirac equation with general hyperbolic Manning-Rosen potential. Energy spectrum is exactly obtained in the closed form and the radial wave functions are expressed in the form of hypergeometric method.

Application of the Frobenius Method to the Schr？dinger Equation for a Spherically Symmetric Hyperbolic Potential

In this paper, an efficient technique for computing the bound state energies and wave functions of the Schrodinger Equation (SE) associated with a new class of spherically symmetric hyperbolic potentials is developed. This technique is based on a recent approximation scheme for the orbital centrifugal term and on the use of the Frobenius method (FM). The bound state eigenvalues are given as zeros of calculable functions. The corresponding eigenfunctions can be obtained by substituting the calculated energies into the recurrence relations for the expanding coefficients of the Frobenius series representing the solution. The excellent performance of this technique is illustrated through numerical results for some special cases like Poschl-Teller potential (PTP), Manning-Rosen potential (MRP) and Poschl-Teller polynomial potential (PTPP), with an application to the Gaussian potential well (GPW). Comparison with other methods is presented. Our results agree noticeably with the previously reported ones.

Some remarks concerning the centrifugal term approximation

We generalize the Pekeris approximation for the centrifugal term potential, l(l+1)r2, and use this to obtain the solutions of the radial Schrödinger equation for the arbitrary angular quantum number, l, of the Hulthén potential. We also obtain the expressions for the bound state energies corresponding to this potential and calculate their values for different states and compare with other results presented in the literature. We also consider some models of physical potentials, namely, the Eckart potential, the Poschl-Teller potentials, the Rosen-Morse potential, the Woods-Saxon potential, and the Manning-Rosen potential. Thus, following straightforward the example corresponding to the Hulthén potential, we show what the radial solutions and the energy spectra for these potentials are.

Path integral solution for a Klein–Gordon particle in vector and scalar deformed radial Rosen–Morse-type potentials

The problem of a Klein–Gordon particle moving in equal vector and scalar Rosen–Morse-type potentials is solved in the framework of Feynman’s path integral approach. Explicit path integration leads to a closed form for the radial Green’s function associated with different shapes of the potentials. For $$q\le -1$$ , and $$\frac{1}{2\alpha }\ln \left| q\right|<r<+\infty$$ , the energy equation and the corresponding wave functions are deduced for the l states using an appropriate approximation to the centrifugal potential term. When $$-1<q<0$$ or $$q>0$$ , it is shown that the quantization conditions for the bound state energy levels $$E_{n_{r}}$$ are transcendental equations which can be solved numerically. Three special cases such as the standard radial Manning–Rosen potential $$(\left| q\right| =1)$$ , the standard radial Rosen–Morse potential $$(V_{2}\rightarrow -V_{2},q=1)$$ and the radial Eckart potential $$(V_{1}\rightarrow -V_{1},q=1)$$ are also briefly discussed.

Analytical solutions of the Klein–Gordon equation for Manning–Rosen potential with centrifugal term through Nikiforov–Uvarov method

We present approximate analytical solutions of the Klein–Gordon equation with arbitrary l state for the Manning–Rosen potential using the Nikiforov–Uvarov method and adopting the approximation scheme for the centrifugal term. We provide the bound state energy spectrum and the wave function in terms of the hypergeometric functions.

Partition function of improved Tietz oscillators

We present a closed-form expression of the vibrational partition function for the improved Tietz potential energy model. The vibrational partition functions for the improved Manning-Rosen potential and improved Rosen-Morse potential are easily deduced as two special cases. The obtained results are applicable to many issues in chemical physics and engineering.

Solution of five dimensional Dirac equation with Asymtotic Iteration Method in the case of pseudo spin symmetry

The relativistic energies of 5 dimensional Dirac equation in the case of pseudo spin symmetry which governed by a sparable non central using the asymtotic iteration method (AIM).The separable five dimensional shape invariant potentials consisted of Hulthen radial potential and Manning-Rosen angular potentials. The relativistic energies were calculated numerically from the relativistic energy equation.

Relativistic Bound and Scattering Amplitude of Spinless Particles in Modified Schioberg Plus Manning–Rosen Potentials

By using an approximation for the centrifugal term, we study relativistic bound and scattering states of spin-zero particles in the presence of equal scalar and vector modified Schioberg plus Manning–Rosen potentials for any quantum numbers n and l. Energy eigenvalues and the scattering amplitude are calculated. Some special cases of the problem are also investigated.

On the arbitrary l-wave solutions of the deformed hyperbolic manning-rosen potential including an improved approximation to the orbital centrifugal term

The arbitrary l-wave solutions to the Schrodinger equation for the deformed hyperbolic Manning-Rosen potential is investigated analytically by using the Nikiforov-Uvarov method, the centrifugal term is treated with an improved Greene and Aldrich’s approximation scheme. The wavefunctions depend on the deformation parameter q, which is expressed in terms of the Jocobi polynomial or the hypergeometric function. The bound state energy is obtained, and the discrete spectrum is shown to be independent of the deformation parameter q.

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.

Relativistic Approximate Solutions for a Two-Term Potential: Riemann-Type Equation

Approximate analytical solutions of a two-term potential are studied for the relativistic wave equations, namely, for the Klein-Gordon and Dirac equations. The results are obtained by solving of a Riemann-type equation whose solution can be written in terms of hypergeometric function 2Fl(a,b; c; z). The energy eigenvalue equations and the corresponding normalized wave functions are given both for two wave equations. The results for some special cases including the Manning-Rosen potential, the Hulthen potential and the Coulomb potential are also discussed by setting the parameters as required.

Linear and nonlinear optical properties in spherical quantum dots: Manning-Rosen potential

In this work, we studied the optical properties of spherical quantum dots confined in Manning-Rosen potential with the appropriate centrifugal term included. The approximate solution of the bound state and wave functions were obtained from the Schrodinger wave equation by applying the standard methods. Also, we have used the density matrix formalism to investigate the linear and third-order nonlinear absorption coefficient and refractive index changes.

Analytical Solution of Dirac Equation for q-Deformed Hyperbolic Manning-Rosen Potential in D Dimensions using SUSY QM and its Thermodynamics'Application

The Dirac equation of q-deformed hyperbolic Manning Rosen potential in D dimension was solved by using Supersymmetric Quantum Mechanics (SUSY QM). The D dimensional relativistic energy spectra were obtained by using SUSY QM and shape invariant properties and D dimensional wave functions of q-deformed hyperbolic Manning Rosen potential were obtained by using the SUSY raising and lowering operators. In the nonrelativistic limit, the relativistic energy spectra for exact spin symmetry case reduced into nonrelativistic energy spectra and so for the wave functions. In the classical regime, the partition function, the vibrational specific heat, and the vibrational mean energy of some diatomic molecules were calculated from the non-relativistic energy spectra with the help of error function and imaginary error function.

Electric quadrupole transitions of the Bohr Hamiltonian with Manning–Rosen potential

Analytical expressions of the wave functions are derived for a Bohr Hamiltonian with the Manning–Rosen potential in the cases of γ-unstable nuclei and axially symmetric prolate deformed ones with γ≈0. By exploiting the results we have obtained in a recent work on the same theme Ref. [1], we have calculated the B(E2) transition rates for 34 γ-unstable and 38 rotational nuclei and compared to experimental data, revealing a qualitative agreement with the experiment and phase transitions within the ground state band and showing also that the Manning–Rosen potential is more appropriate for such calculations than other potentials.

Closed analytical solutions of Bohr Hamiltonian with Manning-Rosen potential model

In the present paper, we have obtained closed analytical expressions for eigenvalues and eigenfunctions of the Bohr Hamiltonian with the Manning–Rosen potential for [Formula: see text]unstable nuclei as well as exactly separable rotational ones with [Formula: see text]. Some heavy nuclei with known [Formula: see text] and [Formula: see text] bandheads have been fitted by using two parameters in the [Formula: see text]unstable case and three parameters in the axially symmetric prolate deformed one. A good agreement with experimental data has been achieved.