Rosen-Morse Potential Research Articles

Analytical Solution of the Klein–Fock–Gordon Equation for the Rosen–Morse Potential

With the help of a successful scheme for overcoming difficulties arising for l ≠ 0 in the centrifugal part of the Rosen–Morse potential with bound states, a solution of the modified Klein–Fock–Gordon equation is found. The energy eigenvalues and the corresponding radial wave functions are found for an arbitrary value of the orbital quantum number ( l ≠ 0 ).

Conformable Fractional of the Analytical Exact Iteration Method for Heavy Quarkonium Masses Spectra

Conformable fractional of the analytical-exact iteration method method is used. The radial Schrodinger equation is analytically solved. Trigonometric Rosen–Morse potential is suggested as a quark-antiquark interaction potential of heavy mesons in the conformable fractional form. The energy eigenvalues and corresponding wave functions are obtained in the N-dimensional space. The effect of fraction-order parameter is studied on the heavy-quarkonium masses such as charmonium and bottomonium. The obtained results are improved in comparison with other theoretical approaches and are in a good agreement with experimental data. Therefore, we show how the fractional parameter acts on the charmonium and bottomonium masses.

Self-localized solitons of a q-deformed quantum system

Beyond a pure mathematical interest, q-deformation is promising for the modeling and interpretation of various physical phenomena. In this paper, we numerically investigate the existence and properties of the self-localized soliton solutions of the nonlinear Schrödinger equation (NLSE) with a q-deformed Rosen–Morse potential. By implementing a Petviashvili method (PM), we obtain the self-localized one and two soliton solutions of the NLSE with a q-deformed Rosen–Morse potential. In order to investigate the temporal behavior and stabilities of these solitons, we implement a Fourier spectral method with a 4th order Runge–Kutta time integrator. We observe that the self-localized one and two solitons are stable and remain bounded with a pulsating behavior and minor changes in the sidelobes of the soliton waveform. Additionally, we investigate the stability and robustness of these solitons under noisy perturbations. A sinusoidal monochromatic wave field modeled within the frame of the NLSE with a q-deformed Rosen–Morse potential turns into a chaotic wavefield and exhibits rogue oscillations due to modulation instability triggered by noise, however, the self-localized solitons of the NLSE with a q-deformed Rosen–Morse potential are stable and robust under the effect of noise. We also show that soliton profiles can be reconstructed after a denoising process performed using a Savitzky–Golay filter.

On an Energy-Dependent Quantum System with Solutions in Terms of a Class of Hypergeometric Para-Orthogonal Polynomials on the Unit Circle

We study an energy-dependent potential related to the Rosen–Morse potential. We give in closed-form the expression of a system of eigenfunctions of the Schrödinger operator in terms of a class of functions associated to a family of hypergeometric para-orthogonal polynomials on the unit circle. We also present modified relations of orthogonality and an asymptotic formula. Consequently, bound state solutions can be obtained for some values of the parameters that define the model. As a particular case, we obtain the symmetric trigonometric Rosen–Morse potential for which there exists an orthogonal basis of eigenstates in a Hilbert space. By comparing the existent solutions for the symmetric trigonometric Rosen–Morse potential, an identity involving Gegenbauer polynomials is obtained.

Confluent second-order supersymmetric quantum mechanics and spectral design

The confluent second-order supersymmetric quantum mechanics, in which the factorization energies tend to a common value, is used to generate Hamiltonians with known spectra departing from the hyperbolic Rosen-Morse and Eckart potentials. The possible spectral modifications, as to create a new level or to delete a given one, as well as the isospectral transformations, are discussed.

Effect of quantum corrections on thermodynamic properties for dimers

We have calculated the effect of quantum correction (QC) on the vibrational partition function by using improved Rosen-Morse potential for Cs2 molecules. The related thermodynamics properties i.e vibrational mean energy, vibrational specific heat, vibrational free energy and vibrational entropy are derived. The change in the partition function and thermodynamic properties by adding quantum corrections up to 20th order are discussed and then compared with their classical counterpart.

Dissipative optical solitons in asymmetric Rosen-Morse potential

We investigate the existence and stability of dissipative soliton solution in a system described by complex Ginzburg-Landau (CGL) equation with asymmetric complex potential, which is obtained from original parity reflection - time reversal (PT) symmetric Rosen-Morse potential. In this study, stability of solution is examined by numerical analysis to show that solitons are stable for some parameter ranges for both self-focusing and self-defocusing nonlinear modes. Dynamical properties such as evolution and transverse energy flow for both modes are also analyzed. Obtained results are useful for experimental designs and applications in related fields.

Trigonometric Rosen–Morse Potential as a Quark–Antiquark Interaction Potential for Meson Properties in the Non-relativistic Quark Model Using EAIM

Trigonometric Rosen-Morse potential is suggested as the quark-antiquark interaction potential for studying the thermodynamic properties and the masses of heavy and heavy-light mesons. For this purpose, N-radial Schrodinger equation is analytically solved using an exact analytical iteration method (EAIM). The eigenvalues of energy and corresponding wave functions are obtained in the N-dimensional space. The present results are applied for calculating the mass of heavy mesons such as charmonium, bottomonium, bc, and cs mesons and thermodynamic properties such as the mean-internal energy, the specific heat, the free energy, and the entropy. The effect of dimensional number is studied on the meson masses. A comparison is studied with other works and experimental data. The present potential provides satisfying results in comparison with other works and experimental data.

Comment on “Solutions of the Dirac equation with an improved expression of the Rosen–Morse potential energy model including Coulomb-like tensor interaction”

The Nikiforov–Uvarov polynomial method employed by Aguda (Can. J. Phys. 2013, 91: 689. doi: 10.1139/cjp-2013-0109 ) to solve the Dirac equation with an improved Rosen–Morse potential plus a Coulomb-like tensor potential is shown to be inappropriate because the conditions of its application are not fulfilled. We clarify the problem and construct the correct solutions in the spin and pseudospin symmetric regimes via the standard method of solving differential equations. For the bound states, we obtain the spinor wave functions in terms of the generalized hypergeometric functions 2F1(a, b, c; z) and in each regime we show that the energy levels are determined by the solutions of a transcendental equation that can be solved numerically.

Superstatistics of Modified Rosen-Morse Potential with Dirac Delta and Uniform Distributions

We discuss the thermodynamic properties of a modified Rosen-Morse potential using the q-deformed superstatistics approaches. We obtain the partition function with the help of the generalized Boltzmann factor from the modified Dirac delta distribution and uniform distribution. Other thermodynamic function is obtained for the superstatistics of the two distributions considered. We also discuss our results graphically and obtain the ordinary statistical quantities when the deformation parameter tends to zero.

Rotation-vibrational energies for some diatomic molecules with improved Rosen-Morse potential in D-dimensions.

By using the Nikiforov-Uvarov method, we solve the Schrödinger equation for the improved Rosen-Morse potential model in D spatial dimensions. We obtained the rotation-vibrational energies and the wave function, respectively. The ro-vibrational energies spectral of NO(a4πi) and [Formula: see text] in D-dimensions have been computed by using the rotation-vibrational energy eigenvalues equation.

Pseudospectral solution of the Schrödinger equation for the Rosen-Morse and Eckart potentials

Pseudospectral methods based on non-classical quadratures are used to numerically compute the eigenvalues and eigenfunctions of the Schrodinger equation for the Rosen-Morse and Eckart potentials. The method uses a basis set of non-classical polynomials, $$\{ P_n(x) \}$$ , orthonormal with respect to a weight function, $$w(x)>0$$ , to construct an $$N \times N$$ matrix representative, $$\{ H_{nm} \}$$ , of the Hamiltonian, H. This matrix representative is transformed to an equivalent pseudospectral representative, $$\{H_{ij}\}$$ . The rate of convergence of the eigenvalues of $$\{ H_{ij} \}$$ to the eigenvalues of H, versus the grid size N, is reported for non-classical basis functions in comparison with the use of Legendre and Laguerre polynomials as well as a Fourier basis. The use of non-classical polynomials is shown to provide the fastest convergence for the eigenvalues. The pseudospectral method based on nonclassical quadratures proposed in this paper should find wide applicability to other problems in quantum and statistical mechanics. A review is provided of the use of a tensor product of one dimensional basis functions to describe two and three dimensional problems.

Generalized squeezed states

Squeezed states are one of the most useful quantum optical models having various applications in different areas, especially in quantum information processing. Generalized squeezed states are even more interesting since, sometimes, they provide additional degrees of freedom in the system. However, they are very difficult to construct and, therefore, people explore such states for individual setting and, thus, a generic analytical expression for generalized squeezed states is yet inadequate in the literature. In this article, we propose a method for the generalization of such states, which can be utilized to construct the squeezed states for any kind of quantum models. Our protocol works accurately for the case of the trigonometric Rosen–Morse potential, which we have considered as an example. Presumably, the scheme should also work for any other quantum mechanical model. In order to verify our results, we have studied the nonclassicality of the given system using several standard mechanisms. Among them, the Wigner function turns out to be the most challenging from the computational point of view. We, thus, also explore a generalization of the Wigner function and indicate how to compute it for a general system like the trigonometric Rosen–Morse potential with a reduced computation time.

Localized analytical solutions and numerically stabilities of generalized Gross–Pitaevskii (GP([formula omitted])) equation with specific external potentials

We present the generalized Gross–Pitaevskii (GP(p,q)) equation with two kinds of specific space–time modulated potentials, including the generalized Rosen–Morse potential, the combination of harmonic and Gaussian (harmonic–Gaussian) potential. Some analytical bright soliton solutions are derived from the generalized GP(p,q) equation via the complex similarity transformation and the generalized stationary nonlinear Schrödinger (NLS) equation. The soliton solutions can be reduced to Jacobi elliptic and spikon-like solutions by choosing the different parameters, and describe some physically relevant phenomenons. Furthermore, some stabilities of the obtained matter-wave solutions are addressed numerically. We find that some solutions are stable and can be observed over a broad range of parameters through analyzing the effect of the phase noise on these solutions. The obtained results may give a certain theoretical guiding significance of relative experiments in Bose–Einstein condensates.

The D-dimensional non-relativistic particle in the Scarf Trigonometry plus Non-Central Rosen-Morse Potentials

The D-Dimensional Non-Relativistic Particle Properties in the Scarf Trigonometry plus Non-Central Rosen-Morse Potentials was investigated using an analytical method. The bound state energy is given approximately in the closed form. The approximate wave function for arbitrary l-state in D-dimensions are expressed in the form of generalised Jacobi Polynomials. The energy spectra of the particle are increased when the dimensions are higher. The relationship between the orbital number in each dimension is recursive. The special case in 3 dimensions is given to the ground state.

Exact Solution of Klein–Gordon and Dirac Equations with Snyder–de Sitter Algebra

In this paper, we present the exact solution of the $$(1+1)$$ -dimensional relativistic Klein–Gordon and Dirac equations with linear vector and scalar potentials in the framework of deformed Snyder–de Sitter model. We introduce some changes of variables, we show that a one-dimensional linear potential for the relativistic system in a space deformed can be equivalent to the trigonometric Rosen–Morse potential in a regular space. In both cases, we determine explicitly the energy eigenvalues and their corresponding eigenfunctions expressed in terms of Romonovski polynomials. The limiting cases are analyzed for $$\alpha _{1}$$ and $$\alpha _{2} \rightarrow 0$$ and are compared with those of literature.

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.

Information Theoretic Global Measures of Dirac Equation With Morse and Trigonometric Rosen–Morse Potentials

In this study, the information-theoretic measures of (1+1)-dimensional Dirac equation in both position and momentum spaces are investigated for the trigonometric Rosen–Morse and the Morse potentials. The solutions of the corresponding Dirac equation are obtained in an exact analytical manner in the first step. Next, using the Fourier transformation, the position and momentum Shannon information entropies are obtained and some features of the probability densities are analyzed. The consistency with Bialynicki-Birula–Mycielski inequality and Heisenberg uncertainty is checked.

Solitons and their stability in the nonlocal nonlinear Schrödinger equation with PT-symmetric potentials.

We report localized nonlinear modes of the self-focusing and defocusing nonlocal nonlinear Schrödinger equation with the generalized PT-symmetric Scarf-II, Rosen-Morse, and periodic potentials. Parameter regions are presented for broken and unbroken PT-symmetric phases of linear bounded states and the linear stability of the obtained solitons. Moreover, we numerically explore the dynamical behaviors of solitons and find stable solitons for some given parameters.