Hyperbolic Potential Research Articles

Quasi-exact treatment of non-relativistic generalized hyperbolic potentials

The solution of the Schrödinger equation for the two quasi-exactly solvable potentials is presented using the Lie algebra approach. It is shown that all models give rise to the same basic differential equation which is quasi-exactly solvable. The eigenvalues, eigenfunctions and the allowed potential parameters are given for each of the two models in terms of the roots of a set of algebraic quasi-exact solvable methods.

The superradiance phenomenon in spin-one particles

In this paper, we solve the Duffin–Kemmer–Petiau (DKP) equation in the presence of hyperbolic tangent potential for spin-one particles. By partitioning the spin-one spinor, we show that the DKP equation is equivalent to the Klein–Gordon equation formalism. The scattering solutions are derived in terms of hypergeometric functions. The reflection [Formula: see text] and transmission [Formula: see text] coefficients are calculated in terms of the Gamma functions. The results show the presence of the superradiance phenomenon when [Formula: see text] for a specific region in the potential becomes greater than one.

Relativistic Symmetries of Bosonic Particles and Antiparticles in the Background of the Position-Dependent Mass for the Improved Deformed Hulthen Plus Deformed Type-Hyperbolic Potential in 3D-EQM Symmetries

The bound state solutions of the deformed Klien-Gordon equation have been determined in the three-dimensional extended relativistic quantum mechanics 3D-ERQM symmetries using position-dependent mass (PDM) with unequal scalar and vector potential for the improved Hulthén plus improved deformed type-hyperbolic potential (PDM-SVID(H-TP)) models. PDM with unequal scalar and vector potential for the Hulthén plus deformed type-hyperbolic potential (PDM-(SVH-DTP)) models, as well as a combination of radial terms, which are coupled with the coupling LΘ, which explains the interaction of the physical features of the system with the topological deformations of space-space. The new relativistic energy eigenvalues have been derived using the parametric Bopp shift method and standard perturbation theory which is sensitive to the atomic quantum numbers (j,l,s,m), mixed potential depths (V0S0V1S1), the rest, and perturbed mass (m0,m1), the screening parameter's inverse α, and noncommutativity parameters (Θ,τ,χ). Within the framework of 3D-ERQM symmetries, we have treated certain significant particular instances that we hope will be valuable to the specialized researcher. We have also treated the nonrelativistic limit and applied our obtained results to generate the mass spectra of heavy-light mesons (HLM) such as cc- and bb- under PDM-SE with improved deformed Hulthén plus improved hyperbolic potential (PDM‑ID(H-TP)) models. When the three simultaneous limits (Θ,τ,χ) were applied, we recovered the normal results of relativistic in the literature ( 0,0,0) for the PDM‑ID(H-TP)) models.

Solutions of the N-dimensional Klein-Gordon Equation with Ultra Generalized Exponential–Hyperbolic Potential to Predict the Mass Spectra of Heavy Mesons

Abstract: We solved the N-dimensional Klein-Gordon equation analytically using the Nikiforov-Uvarov method to obtain the energy eigenvalues and the corresponding wave function in terms of Laguerre polynomials with the ultra generalized exponential–hyperbolic potential. The present results are applied for calculating the mass spectra of heavy mesons, such as charmonium (cc ̅) and bottomonium (bb ̅), for different quantum states. The present work provides excellent results in comparison with experimental data with a maximum error of 0.0059GeV and the works of other researchers. Keywords: Ultra generalized exponential–hyperbolic potential, Klein-Gordon equation, Heavy mesons, Nikiforov-Uvarov method.

Quantum Information Entropy of Hyperbolic Potentials in Fractional Schrödinger Equation.

In this work we have studied the Shannon information entropy for two hyperbolic single-well potentials in the fractional Schrödinger equation (the fractional derivative number (0<n≤2) by calculating position and momentum entropy. We find that the wave function will move towards the origin as the fractional derivative number n decreases and the position entropy density becomes more severely localized in more fractional system, i.e., for smaller values of n, but the momentum probability density becomes more delocalized. And then we study the Beckner Bialynicki-Birula−Mycieslki (BBM) inequality and notice that the Shannon entropies still satisfy this inequality for different depth u even though this inequality decreases (or increases) gradually as the depth u of the hyperbolic potential U1 (or U2) increases. Finally, we also carry out the Fisher entropy and observe that the Fisher entropy increases as the depth u of the potential wells increases, while the fractional derivative number n decreases.

Computing thermodynamic properties of some diatomic molecules using a q-deformed Scarf-like potential

This paper computes the vibrational partition function of some diatomic molecules using an improved energy spectrum obtained recently with the q-deformed hyperbolic Scarf-like potential. Compared to the experimental energy curves, this potential proved to represent well the interaction between the atoms in the studied molecules. The related thermodynamic functions are derived for the , ScI and molecules. Results demonstrated that the computed molecular entropy is in very good agreement with the experimental data for a large range of temperature values. In addition, results are given for the ScI molecule for which no experimental entropy values exist. Our results can serve as a reference to experimental studies in chemical physics.

Cosmological inflation in f(Q,T) gravity

We study the cosmological inflation within the context of f(Q, T) gravity, wherein Q is the nonmetricity scalar and T is the trace of the matter energy-momentum tensor. By choosing a linear combination of Q and T, we first analyze the realization of an inflationary scenario driven via the geometrical effects of the linear f(Q, T) gravity and then, we obtain the modified slow-roll parameters, the scalar and the tensor spectral indices, and the tensor-to-scalar ratio for the proposed model. In addition, by choosing three inflationary potentials, i.e. the power-law, hyperbolic and natural potentials, and by applying the slow-roll approximations, we calculate these inflationary observables in the presence of an inflaton scalar field. The results indicate that by properly restricting the free parameters, the proposed model provides appropriate predictions that are consistent with the observational data obtained from the Planck 2018. Also, we specify that the contribution of linear model of f(Q, T) gravity with the hyperbolic and natural potentials can impose different restrictions on the parameters of these potentials. Furthermore, the predictions of natural inflation in this model are in good agreement with the joint Planck, BK15 and BAO data, justifying the use of the f(Q, T) gravity.

Solusi Persamaan Schrodinger dengan Potensial Scraf II Hyperbolic menggunakan Pendekatan Semiklasik

The particle system is affected by the Scraf II Hyperbolic potential. The solution for solving the Schrodinger equation with the Scraff II Hyperbolic potential uses a semiclassical approach, namely using the WKB approach. The WKB approach is used to obtain an equation for the energy spectrum that is affected by the Scraf II Hyperbolic potential. Keywords: The Schrodinger equation, Hyperbolic Scraf II potential, WKB approach

Quantum information entropies for a soliton at hyperbolic well

In this work, the probability uncertainties related to a stationary quantum system with solitonic mass distribution when subjected to deformable hyperbolic potentials are studied. Shannon’s entropy and Fisher’s information of a position-dependent mass are calculated. To investigate the concept of Shannon and Fisher entropies of the solitonic mass distribution subject to the hyperbolic potential, it is necessary to obtain the analytic solutions at position and momentum space. For the Hamiltonian operator to be Hermitian, we consider the stationary Schrödinger equation ordered by Zhu–Kroemer. This ordering is known to describe abrupt heterojunctions in semiconductor materials.

Quasi-exact solutions for guided modes in two-dimensional materials with tilted Dirac cones

We show that if the solutions to the (2+1)-dimensional massless Dirac equation for a given one-dimensional (1D) potential are known, then they can be used to obtain the eigenvalues and eigenfunctions for the same potential, orientated at an arbitrary angle, in a 2D Dirac material possessing tilted, anisotropic Dirac cones. This simple set of transformations enables all the exact and quasi-exact solutions associated with 1D quantum wells in graphene to be applied to the confinement problem in tilted Dirac materials such as 8-Pmmn borophene. We also show that smooth electron waveguides in tilted Dirac materials can be used to manipulate the degree of valley polarization of quasiparticles travelling along a particular direction of the channel. We examine the particular case of the hyperbolic secant potential to model realistic top-gated structures for valleytronic applications.

Quantum Information Entropies on Hyperbolic Single Potential Wells.

In this work, we study the quantum information entropies for two different types of hyperbolic single potential wells. We first study the behaviors of the moving particle subject to two different hyperbolic potential wells through focusing on their wave functions. The shapes of these hyperbolic potentials are similar, but we notice that their momentum entropy densities change along with the width of each potential and the magnitude of position entropy density decreases when the momentum entropy magnitude increases. On the other hand, we illustrate the behaviors of their position and momentum entropy densities. Finally, we show the variation of position and momentum entropies and with the change of the potential well depth u and verify that their sum still satisfies the BBM inequality relation.

Approximate Solutions, Thermal Properties, and Superstatistics Solutions to Schrödinger Equation

In this work, we apply the parametric Nikiforov-Uvarov method to obtain eigensolutions and total normalized wave function of Schrödinger equation expressed in terms of Jacobi polynomial using Coulomb plus Screened Exponential Hyperbolic Potential (CPSEHP), where we obtained the probability density plots for the proposed potential for various orbital angular quantum number, as well as some special cases (Hellmann and Yukawa potential). The proposed potential is best suitable for smaller values of the screening parameter α . The resulting energy eigenvalue is presented in a close form and extended to study thermal properties and superstatistics expressed in terms of partition function Z and other thermodynamic properties such as vibrational mean energy U , vibrational specific heat capacity C , vibrational entropy S , and vibrational free energy F . Using the resulting energy equation and with the help of Matlab software, the numerical bound state solutions were obtained for various values of the screening parameter ( α ) as well as different expectation values via Hellmann-Feynman Theorem (HFT). The trend of the partition function and other thermodynamic properties obtained for both thermal properties and superstatistics were in excellent agreement with the existing literatures. Due to the analytical mathematical complexities, the superstatistics and thermal properties were evaluated using Mathematica 10.0 version software. The proposed potential model reduces to Hellmann potential, Yukawa potential, Screened Hyperbolic potential, and Coulomb potential as special cases.

Manipulating two-dimensional solitons in inhomogeneous nonlinear Schrödinger equation with power-law nonlinearity under [formula omitted]-symmetric Rosen–Morse and hyperbolic Scarff-II potentials

We construct two-dimensional soliton solutions for the inhomogeneous nonlinear Schrödinger (NLS) equation with power-law nonlinearity in two different types of parity-time (PT)-symmetric potentials, namely Rosen–Morse and hyperbolic Scarff-II potentials, through a similarity transformation. In each case, following three different kinds of dispersion parameters are considered: (i) exponential, (ii) periodic, and (iii) hyperbolic. We investigate the impact on the dynamical characteristics of solitons by varying the strengths of the inhomogeneity parameter. We also analyse the intensity variations of solitons at different propagation distances for three distinct dispersion profiles. Further, we observe that the intensity distribution of solitons stretches in space and that the width of it increases as the value of the power-law nonlinearity parameter increases. Our findings reveal that the obtained soliton solutions can be managed with the help of the strengths of both PT-symmetric potentials and dispersion parameters.

Quantum information for a solitonic particle with hyperbolic interaction

In this work, we analyze a particle with position-dependent mass, with solitonic mass distribution in a stationary quantum system, for the particular case of the BenDaniel–Duke ordering, in a hyperbolic barrier potential. The kinetic energy ordering of BenDaniel–Duke guarantees the hermiticity of the Hamiltonian operator. We find the analytical solutions of the Schrödinger equation and their respective quantized energies. In addition, we calculate the Shannon entropy and Fisher information for the solutions in the case of the lowest energy states of the system.

Route to Chaos in Discrete Two-dimensional Maps with Hyperbolic Double-well Potentials

Route to Chaos in Discrete Two-dimensional Maps with Hyperbolic Double-well Potentials

Quasi-exactly solvable hyperbolic potential and its anti-isospectral counterpart

We solve the eigenvalue spectra for two quasi exactly solvable (QES) Schrödinger problems defined by the potentials V(x;γ,η)=4γ2cosh4(x)+V1(γ,η)cosh2(x)+ηη−1tanh2(x) and U(x;γ,η)=−4γ2cos4(x)−V1(γ,η)cos2(x)+ηη−1tan2(x), found by the anti-isospectral transformation of the former. We use three methods: a direct polynomial expansion, which shows the relation between the expansion order and the shape of the potential function; direct comparison to the confluent Heun equation (CHE), which has been shown to provide only part of the spectrum in different quantum mechanics problems, and the use of Lie algebras, which has been proven to reveal hidden algebraic structures of this kind of spectral problems.

Feynman kernel analytical solutions for the deformed hyperbolic barrier potential with application to some diatomic molecules

In this paper, we derive the ℓ-states energy spectrum of the q-deformed hyperbolic Barrier Potential. Within the Feynman path integral formalism, we propose an appropriate approximation of the centrifugal term. Then, using Euler angles and the isomorphism between Λ3 and SU(1, 1), we convert the radial path integral into a maniable one. The obtained eigenvalues are in very good agreement with the numerical results. In addition, we applied our results to some diatomic molecules and obtained accurate results compared to the experimental (RKR) values.

Solitonic model of the condensate

We consider a spatially extended box-shaped wave field that consists of a plane wave (the condensate) in the middle and equals zero at the edges, in the framework of the focusing one-dimensional nonlinear Schrodinger equation. Within the inverse scattering transform theory, the scattering data for this wave field is presented by the continuous spectrum of the nonlinear radiation and the soliton eigenvalues together with their norming constants; the number of solitons N is proportional to the box width. We remove the continuous spectrum from the scattering data and find analytically the specific corrections to the soliton norming constants that arise due to the removal procedure. The corrected soliton parameters correspond to symmetric in space N-soliton solution, as we demonstrate analytically in the paper. Generating this solution numerically for N up to 1024, we observe that, at large N, it converges asymptotically to the condensate, representing its solitonic model. Our methods can be generalized for other strongly nonlinear wave fields, as we demonstrate for the hyperbolic secant potential, building its solitonic model as well.

Optical properties of a GaAs quantum well with new type of hyperbolic confinement potential: Effect of structure parameters and intense laser field

In this present study, we have investigated theoretically the effect of structure parameters (η and κ) and high-frequency intense laser field (ILF) on the linear and nonlinear optical properties of a GaAs quantum well (QW) with new type of hyperbolic confinement potential. Within the framework of the effective-mass and parabolic band approximations, we have computed the confined subband energy levels and their corresponding densities of probability by using the diagonalization method. Besides, we evaluated the total optical absorption coefficients (TOACs) and total refractive index changes (TRICs). The obtained numerical findings show that an increase of the η (κ) structure parameter causes an increase (decrease) in amplitude in TOACs and a blue (red) shift of the resonance energy spectrum. In addition, with the increase of the ILF, the resonance energy spectrum shifts to blue, while the amplitude of TOACs (TRICs) increased (decreased). We think that the obtained these results can be useful in the design of new device’s generation employed in optoelectronic domain.

L-states solutions for the q-deformed Scarf potential with path integrals formulation

In this paper, we solve the Feynman Kernel for the q-deformed hyperbolic Scarf potential for any ℓ-states. We propose an accurate generalization of the Pekeris approximation of the centrifugal term adapted to deformed potentials which allows to transform our potential to a solvable shifted modified Pöschl-Teller one. Analytical expressions of the energy spectrum and the normalized ℓ-state eigenfunctions are derived from the Green function. We evaluate and compare our results to the literature. Furthermore, we apply our method in chemical physics to derive the spectrum of some diatomic molecules. We obtained good results compared to state-of-the-art competing analytical and numerical methods.