Rosen-Morse Potential Research Articles

Rosen-Morse potential and gravitating kinks

We show that in a special type of two-dimensional dilaton-gravity-scalar model, where both the dilaton and the scalar matter fields have noncanonical kinetic terms, it is possible to construct kink solutions whose linear perturbation equation is a Schrödinger-like equation with Rosen-Morse potential. For this potential, eigenvalues and wave functions of the bound states, if had any, can be derived by using the standard shape invariance procedure. Depending on the values of the parameters, the stability potential can be reflective or reflectionless. There can be an arbitrary number of shape modes, but the zero mode is always absent.

Non-relativistic energy spectra of and diatomic molecules confined in a modified Scarf potential via supersymmetric WKB approach

In this research, the energy equation of the Schrodinger equation with the modified Scarf potential has been obtained using the supersymmetric WKB (SWKB) approach. The Pekeris approximation has been applied to enable the analytical solution. The energy equation was applied to determine the rovibrational states of two diatomic molecules such as O 2 + ( X 2 Π g ) and N 2 ( X 1 Σ g + ) . The average kinetic and potential energies were computed via the Hellman-Feynman theorem. The analytical result of the energy equation obtained coincides with the work reported in earlier literature where the authors had applied a different approach. The energy eigenvalues for the studied molecules were found to agree with the ones obtained using the Teitz-Hua molecular potential, the deformed modified Rosen-Morse (DMRM) potential, the Morse potential and the Rydberg-Klein-Rees data points. For the energy spectra, we found average absolute deviations of 0.129515% for O 2 + ( X 2 Π g ) and 1.834993% for N 2 ( X 1 Σ g + ) molecules respectively. The energy spectra increase as the quantum numbers increase up to the dissociation limit before decreasing. For the molecules, the atoms were found to possess an oscillatory-type motion where an increase in the mean kinetic energy resulted in a decrease in mean potential energy and vice-visa.

Beam propagation in cubic-quintic nonlinear optical system supported by modified parity-time symmetric Rosen-Morse complex potential.

The present study explores the stability and persistence of nonlinear waves in self-focusing cubic-quintic media employing couplings of nonlinearity, spatial diffraction, and the parity-time symmetric Rosen-Morse complex field. Here, we discover that a system supported by Rosen-Morse potential can develop eigenmodes but does not accommodate stable soliton solutions for any potential parameters due to the non-vanishing terms in the imaginary component of potential. The study expands by modifying Rosen-Morse potential and discovers that the region of sustained PT-symmetry in the self-focusing material is enhanced and influenced by the order of the nonlinear function, spectral filtering, and gain/loss in the system. Stable soliton conditions for both broken PT-symmetric and PT-symmetric regions are established by the linear stability analysis using numerical simulations. Nonlinear propagation of the beam in the modified PT system is explored and identifies that stable beam propagation is possible only if the system is supported by the field, which is below the threshold imaginary potential.

Massive Dirac particles based on gapped graphene with Rosen–Morse potential in a uniform magnetic field

Abstract In this paper, we explore the gapped graphene structure in the two-dimensional plane in the presence of the Rosen-Morse potential and the external uniform magnetic field. In order to describe the corresponding structure, we consider the propagation of electrons in graphene as relativistic fermion quasi-particles, and analyze it by the wave functions of two-component spinors with pseudo-spin symmetry using the Dirac equation. Next, to solve and analyze the Dirac equation, we obtain the eigenvalues and eigenvectors using the Legendre differential equation. After that, we obtain the bounded states of energy depending on the coefficients of Rosen-Morse and magnetic potentials in terms of quantum numbers of principal n and spin-orbit k. Then, the values of the energy spectrum for the ground state and the first excited state are calculated, and the wave functions and the corresponding probabilities are plotted in terms of coordinates r. In what follows, we explore the band structure of gapped graphene by the modified dispersion relation and write it in terms of the two-dimensional wave vectors K x and K y . Finally, the energy bands are plotted in terms of the wave vectors K x and K y with and without the magnetic term.

Simultaneous effects of the position dependent mass and magnetic field on quantum well with the improved Tietz potential

In this study, we explored the synergistic impact of position-dependent mass and magnetic field on the electronic and optical properties of quantum wells, featuring an enhanced Tietz potential confinement incorporating both standard Morse and improved Rosen–Morse potentials, as influenced by variations in the structural parameter. Calculations were conducted within the framework of effective mass and parabolic band approximations. The diagonalization method was employed, selecting a wave function basis of trigonometric orthonormal functions to determine the eigenvalues and eigenfunctions of the confined electron potential. Our findings reveal that alterations in the sizes and shapes of the quantum wells, magnetic field strength, geometric asymmetry, and confinement parameters lead to significant variations in electron energies, transition between electron states, and the absorption spectrum. These outcomes offer valuable insights for investigating the electronic and structural properties of materials and devising novel materials with tailored optical characteristics.

Electronic and optical properties of the exponential and hyperbolic Rosen–Morse types quantum wells under applied magnetic field

In this study, we considered the electronic and optical properties of quantum wells with the exponential and hyperbolic Rosen–Morse potentials under an applied magnetic field. Calculations are made within the framework of effective mass and parabolic band approximations. We have used the diagonalization method by choosing a wave function based on the trigonometric orthonormal function to find eigenvalues and eigenfunctions of the confined electron. Our results show that the magnetic field, asymmetry, and confinement parameters cause a significant increase in electron energies and energy differences between the electron states and the blue shift in the absorption peaks. These results can be used to probe materials’ electronic and structural properties and develop new materials with tailored optical properties.

Position-Dependent Effective Mass and Asymmetry Effects on the Electronic and Optical Properties of Quantum Wells with Improved Rosen–Morse Potential

In this study, we investigated, for the first time, the effects of the spatially varying effective mass, asymmetry parameter, and well width on the electronic and optical properties of a quantum well which has an improved Rosen–Morse potential. Calculations were made within the framework of the effective mass and parabolic band approximations. We have used the diagonalization method by choosing a wave function based on the trigonometric orthonormal functions to find eigenvalues and eigenfunctions of the electron confined within the improved Rosen–Morse potential. Our results show that the position dependence mass, asymmetry, and confinement parameters cause significant changes in the electronic and optical properties of the structure we focus on since these effects create a significant increase in electron energies and a blue shift in the absorption spectrum. The increase in energy levels enables the development of optoelectronic devices that can operate at wider wavelengths and absorb higher-energy photons. Through an appropriate choice of parameters, the Rosen–Morse potential offers, among many advantages, the possibility of simulating heterostructures close to surfaces exposed to air or vacuum, thus giving the possibility of substantially enriching the allowed optical transitions given the breaking of the system´s symmetries. Similarly, the one-dimensional Rosen–Morse potential model proposed here can be extended to one- and zero-dimensional structures such as core/shell quantum well wires and quantum dots. This offers potential advancements in fields such as optical communication, imaging technology, and solar cells.

The Parametric Generalized Fractional Nikiforov-Uvarov Method and Its Applications

By using generalized fractional derivative, the parametric generalized fractional Nikiforov-Uvarov (NU) method is introduced. The second-order parametric generalized differential equation is exactly solved in the fractional form. The obtained results are applied on the extended Cornell potential, the pesudoharmonic potential, the Mie potential, the Kratzer-Fues potential, the harmonic oscillator potential, the Morse potential, the Woods-Saxon potential, the Hulthen potential, the deformed Rosen-Morse potential and the P schl-Teller potential which play an important role in the fields of molecular and atomic physics. The special of classical cases are obtained from the fractional cases at which are agreement with recent works.

A precise estimation for vibrational energies of diatomic molecules using the improved Rosen–Morse potential

In the context of the generalized fractional derivative, novel solutions to the D-dimensional Schrödinger equation are investigated via the improved Rosen-Morse potential (IRMP). By applying the Pekeris-type approximation to the centrifugal term, the generalized fractional Nikiforov-Uvarov method has been used to derive the analytical formulations of the energy eigenvalues and wave functions in terms of the fractional parameters in D-dimensions. The resulting solutions are employed for a variety of diatomic molecules (DMs), which have numerous uses in many fields of physics. With the use of molecular parameters, the IRMP is utilized to reproduce potential energy curves for numerous DMs. The pure vibrational energy spectra for several DMs are determined using both the fractional and the ordinary forms to demonstrate the effectiveness of the method utilized in this work. As compared to earlier investigations, it has been found that our estimated vibrational energies correspond with the observed Rydberg-Klein-Rees (RKR) data much more closely. Moreover, it is observed that the vibrational energy spectra of different DMs computed in the existence of fractional parameters are superior to those computed in the ordinary case for fitting the observed RKR data. Thus, it may be inferred that fractional order significantly affects the vibrational energy levels of DMs. Both the mean absolute percentage deviation (MAPD) and average absolute deviation (AAD) are evaluated as the goodness of fit indicators. According to the estimated AAD and MAPD outcomes, the IRMP is an appropriate model for simulating the RKR data for all of the DMs under investigation.

Solitons in fourth-order Schrödinger equation with parity-time-symmetric extended Rosen-Morse potentials

We investigate the fourth-order nonlinear Schrödinger equation modulated by parity-time-symmetric extended Rosen-Morse potentials. Since the imaginary part of the potentials does not vanish asymptotically, any slight fluctuations in the field can eventually cause the nonlinear modes to become unstable. Here we obtain stable solitons by adding the constraints of coefficients, which make the imaginary part of the potentials component vanish asymptotically. Furthermore, we get other fundamental stable single-hump and double-hump solitons by numerical methods. Then we consider excitations of the soliton via adiabatical change of system parameters. The results we obtained in this work provide a way to search for stable localized modes in parity-time-symmetric extended Rosen-Morse potentials with fourth-order dispersion.

The Dirac equation with /non--symmetric potentials in curved spacetime backgrounds

In this paper, we have presented the Dirac equation in the frame of position-dependent mass on two dimensional gravitational static background in the presence of /non--symmetric potential interactions. The exponential metric component have formed the reduced Dirac operator into the general supersymmetric model within mass changing with coordinates. We have obtained the eigenvalues of the Dirac operator for the complex Morse and trigonometric complex Scarf-II potentials SL(2, C) using Lie algebras and the supersymmetric quantum mechanical approaches. Moreover, after obtaining a general Sturm-Liouville type equation using a convenient mapping, the system have become available to be investigated within η- pseudo-Hermiticity. With this context, η operator is found for the examples of complex trigonometric Rosen-Morse potential and complex Morse potentials with real and complex parameters of the initial system and finally the solutions are obtained for each model with the graphics of energy values and probability densities.

Petviashvili Method for the Fractional Schrödinger Equation

In this paper, we extend the Petviashvili method (PM) to the fractional nonlinear Schrödinger equation (fNLSE) for the construction and analysis of its soliton solutions. We also investigate the temporal dynamics and stabilities of the soliton solutions of the fNLSE by implementing a spectral method, in which the fractional-order spectral derivatives are computed using FFT (Fast Fourier Transform) routines, and the time integration is performed by a 4th order Runge–Kutta time-stepping algorithm. We discuss the effects of the order of the fractional derivative, α, on the properties, shapes, and temporal dynamics of the soliton solutions of the fNLSE. We also examine the interaction of those soliton solutions with zero, photorefractive and q-deformed Rosen–Morse potentials. We show that for all of these potentials, the soliton solutions of the fNLSE exhibit a splitting and spreading behavior, yet their dynamics can be altered by the different forms of the potentials and noise considered.

Heavy-Light Meson Masses in the Framework of Trigonometric Rosen-Morse Potential Using the Generalized Fractional Derivative

Trigonometric Rosen-Morse Potential is employed as a mesonic potential interaction. The extended Nikiforov-Uvarov method is used to solve the N-radial Fractional Schrödinger equation analytically. Using the generalized fractional derivative, the energy eigenvalues are obtained in fractional forms. The current findings are used to calculate the masses of mesons such as charmonium, bottomonium, and heavy-light mesons. The current findings are superior to those of other recent studies and show good agreement with experimental data as a result, the fractional parameter is crucial in optimizing meson masses.

Eigen-solutions and thermal properties of multi-parameter exponential potential

In this work, we determined an approximate eigen solutions of Modified multi-parameter exponential potential using supersymmetric quantum mechanics approach (SUSY) with improved Greene-Aldrich approximation to the centrifugal term. The energy equation and its corresponding normalised radial wave function were fully obtained. The proposed potential reduces to other useful potentials like Rosen-Morse, Hellmann, Yukawa and Coulomb potential as special cases. The thermodynamic properties like the vibrational mean energy (Uβ,V), Vibrational heat capacity (Cβ,V), vibrational entropy (Sβ,V) and vibrational free energy (Fβ,V) of the interacting potential were studied via partition function (Zβ,V) obtained from the resulting energy equation. This study was applied to three diatomic molecules: Chromium hydride (CrH), Titanium Hydride (TiH) and Thiocynate (ScN). To ascertain the high degree of our analytical mathematical accuracy, we compared the results of special cases with an existing results. These were found to be in excellent agreement with the existing results.

Data driven soliton solution of the nonlinear Schrödinger equation with certain P T-symmetric potentials via deep learning.

We investigate the physics informed neural network method, a deep learning approach, to approximate soliton solution of the nonlinear Schrödinger equation with parity time symmetric potentials. We consider three different parity time symmetric potentials, namely, Gaussian, periodic, and Rosen-Morse potentials. We use the physics informed neural network to solve the considered nonlinear partial differential equation with the above three potentials. We compare the predicted result with the actual result and analyze the ability of deep learning in solving the considered partial differential equation. We check the ability of deep learning in approximating the soliton solution by taking the squared error between real and predicted values. Further, we examine the factors that affect the performance of the considered deep learning method with different activation functions, namely, ReLU, sigmoid, and tanh. We also use a new activation function, namely, sech, which is not used in the field of deep learning, and analyze whether this new activation function is suitable for the prediction of soliton solution of the nonlinear Schrödinger equation for the aforementioned parity time symmetric potentials. In addition to the above, we present how the network's structure and the size of the training data influence the performance of the physics informed neural network. Our results show that the constructed deep learning model successfully approximates the soliton solution of the considered equation with high accuracy.

More accurate ro-vibrational energies for SiF +(X 1Σ+) molecule

The most appropriate potential energy function for the X 1Σ+ state of SiF+ molecule has been specified by comparing the vibrational energies obtained via special cases of the general molecular potential (GMP) which are Morse, improved Rosen-Morse, modified Rosen-Morse, improved Manning-Rosen and Tietz potentials with the vibrational energies obtained in the presence of improved generalized Pöschl-Teller (IGPT) potential and experimental data. It has been shown that the improved Rosen-Morse potential is better than the other well-known potential energy functions in fitting experimental energies of SiF +(X 1Σ+) molecule. By using relativistic rotational-vibrational energy eigenvalue relation for Rosen-Morse potential in improved form which is acquired by solving the Dirac equation under the GMP and Pekeris type approximation, the more accurate ro-vibrational energies of SiF +(X 1Σ+) molecule have been obtained. It has been demonstrated for SiF +(X 1Σ+) molecule that in order to procure more proper ro-vibrating energies for the SiF +(X 1Σ+) molecule, a Pekeris-type approach to the centrifugal term is better than the improved Greene-Aldrich in getting more accurate ro-vibrational energies.

Spectral manipulation of the trigonometric Rosen-Morse potential through supersymmetry

The first and second-order supersymmetry transformations can be used to manipulate one or two energy levels of the initial spectrum when generating new exactly solvable Hamiltonians from a given initial potential. In this paper, we will construct the first and second-order supersymmetric partners of the trigonometric Rosen-Morse potential. Firstly, it is identified a set of solutions of the initial stationary Schrödinger equation which are appropriate for implementing in a simple way non-singular transformations, without inducing new singularities in the built potential. Then, the way the spectral manipulation works is illustrated through several specific examples.

Pseudospin symmetric solutions of the Dirac equation with the modified Rosen–Morse potential using Nikiforov–Uvarov method and supersymmetric quantum mechanics approach

Employing the Pekeris-type approximation to deal with the pseudo-centrifugal term, we analytically study the pseudospin symmetry of a Dirac nucleon subjected to equal scalar and vector modified Rosen–Morse potential including the spin–orbit coupling term by using the Nikiforov–Uvarov method and supersymmetric quantum mechanics approach. The complex eigenvalue equation and the total normalized wave functions expressed in terms of Jacobi polynomial with arbitrary spin–orbit coupling quantum number k are presented under the condition of pseudospin symmetry. The eigenvalue equations for both methods reproduce the same result to affirm the mathematical accuracy of analytical calculations. The numerical solutions obtained for different adjustable parameters produce degeneracies for some quantum number.

Nonlinear tunneling of solitons in a variable coefficients nonlinear Schrödinger equation with $$\mathscr {PT}$$-symmetric Rosen–Morse potential

Nonlinear tunneling of solitons in a variable coefficients nonlinear Schrödinger equation with $$\mathscr {PT}$$-symmetric Rosen–Morse potential

Thermodynamic properties of the trigonometric Rosen–Morse potential and applications to a quantum gas of mesons

In this study, we work out thermodynamic functions for a quantum gas of mesons described as color-electric charge dipoles. They refer to a particular parametrization of the trigonometric Rosen–Morse potential which allows to transform it to a perturbation of free quantum motion on the three-dimensional hypersphere, [Formula: see text], a manifold that can host only charge-neutral systems, the charge dipoles being the configuration of the minimal number of constituents. To the amount charge neutrality manifests itself as an important aspect of the color confinement in the theory of strong interaction, the Quantum Chromodynamics, we expect our findings to be of interest to the evaluation of temperature phenomena in the physics of hadrons and in particular in a quantum gas of color charge dipoles as are the mesons. The results are illustrated for [Formula: see text] and [Formula: see text] mesons.