Mie-type Potential Research Articles

Topological effects of cosmic string on radial eigenvalue solution with Mie-type potential

Topological effects of cosmic string on radial eigenvalue solution with Mie-type potential

Topological effects on non-relativistic eigenvalue solutions under AB-flux field with pseudoharmonic- and Mie-type potentials

In this paper, we investigate the quantum dynamics of a non-relativistic particle confined by the Aharonov–Bohm quantum flux field with pseudoharmonic-type potential in the background of topological defect produced by a point-like global monopole. We solve the radial Schrödinger equation analytically and determine the exact eigenvalue solution of the quantum system. Afterwards, we consider a Mie-type potential in the quantum system and solve the radial equation analytically and obtain the eigenvalue solution. We analyze the effects of the topological defect and the quantum flux with these potentials on the energy eigenvalue and wave function of the non-relativistic particles. In fact, it is shown that the energy levels and wave functions are influenced by the topological defect shifted the result compared to the flat space results. In addition, the quantum flux field also shifted the eigenvalue solutions and an analogue of the Aharonov–Bohm effect for bound-states is observed. Finally, we utilize these eigenvalue solutions to some known diatomic molecular potential models and presented the energy eigenvalue and wave function.

Point-like defect on Schrödinger particles under flux field with harmonic oscillator plus Mie-type potential: application to molecular potentials

In this analysis, we study the quantum motions of a non-relativistic particle confined by the Aharonov–Bohm (AB) flux field with harmonic oscillator plus Mie-type potential in a point-like defect. We determine the eigenvalue solution of the particles analytically and discuss the effects of the topological defect and flux field with this potential. This eigenvalue solution is then used in some diatomic molecular potential models (harmonic oscillator plus Kratzer, modified Kratzer and attractive Coulomb potentials) and presented as the eigenvalue solutions. Afterwards, we consider a general potential form (superposition of pseudoharmonic plus Cornell-type potential) in the quantum system and analyse the effects of various factors on the eigenvalue solution. It is shown that the eigenvalue solutions are modified by the topological defect of a point-like global monopole and flux field compared to the results obtained in the flat space.

Deformed Dirac and Shrödinger Equations with Improved Mie-Type Potential for Diatomic Molecules and Fermionic Particles in the Framework of Extended Quantum Mechanics Symmetries

In this study, the bound-state solutions of the deformed Dirac equation (DDE) have been determined with the improved Mie-type potential including an improved Coulomb-like tensor potential (IMTPICLP) under the condition of the spin or pseudospin symmetry in the extended relativistic quantum mechanics (ERQM) symmetries. The IMTPICLP model includes a combination of the terms 1/r3 and 1/r4 which coupled with the couplings (LΘ and L̃︀Θ) between the physical properties of the system with the topological deformations of space-space. In the framework of the parametric Bopp’s shift method and standard perturbation theory, the new relativistic and nonrelativistic energy eigenvalues for the improved Mietype potential have been found. The new obtained values appeared sensitive to the quantum numbers (j, k, l,̃︀ l, s, s,̃︀ m, m̃︀ ), the mixed potential depths (A, B, C, α), and noncommutativity parameters (Θ, σ, χ). The new energy spectra of the improved Kratzer–Fues potential within an improved Coulomb-like tensor interaction and the improved modified Kratzer potential within the Coulomb-like tensor interaction have been derived as particular cases of IMTPICLP. We recovered the usual relativistic and nonrelativistic results from the literature by applying the three simultaneous limits (Θ, σ, χ) → (0, 0, 0). One can notice that our results are in close agreement with the recent studies.

Exact solutions of the Schrödinger equation with Dunkl derivative for the free-particle spherical waves, the pseudo-harmonic oscillator and the Mie-type potential

In this paper, we solve exactly the Schrödinger equation for the free-particle, the pseudo-harmonic oscillator and the Mie-type potential in three dimensions with the Dunkl derivative. The equations for the radial and angular parts are obtained by using spherical coordinates and separation of variables. The wave functions and the energy spectrum for these potentials are derived in an analytical way and it is shown that our results are adequately reduced to those previously reported when we remove the Dunkl derivative parameters.

On the position-dependent mass Schrödinger equation for Mie-type potentials

The exactly solvable Position Dependent Mass Schrödinger Equation (PDMSE) for Mie-type potentials is presented. To that, by means of a point canonical transformation the exactly solvable constant mass Schrödinger equation is transformed into a PDMSE. The mapping between both Schrödinger equations lets obtain the energy spectra and wave functions for the potential under study. This happens for any selection of the O von Roos ambiguity parameters involved in the kinetic energy operator. The exactly solvable multiparameter exponential-type potential for the constant mass Schrödinger equation constitutes the reference problem allowing to solve the PDMSE for Mie potentials and mass functions of the form given by m(x) = skx s-1/(xs + 1))2. Thereby, as a useful application of our proposal, the particular Lennard-Jones potential is presented as an example of Mie potential by considering the mass distribution m(x) = 6kx 5/(x 6 + 1))2. The proposed method is general and can be straightforwardly applied to the solution of the PDMSE for other potential models and/or with different position-dependent mass distributions.

Quasi-exact solution of the Dirac equation on curved space-time with Coulomb scalar and vector potentials and Mie-type tensor potential with pseudo-spin and spin symmetries

In this paper we solve the Dirac equation with the Coulomb scalar U(r) and vector V(r) potentials and type-Mie tensor potential in curved space-time whose metric is of type with spherical symmetry. For this we consider two types of symmetry in the system, first spin symmetry with V(r) = U(r) and then with pseudo-spin symmetry V(r) = − U(r). In both cases we have a tensor potential A(r) that coupling through the electromagnetic field A μ = (V(r), cA(r), 0, 0). We find, quasi-exactly, the Dirac spinor and the energy spectrum of the system, and we sketch the probability densities and some energy spectra.

Solution of the Ultra Generalized Exponential–Hyperbolic Potential in Multi-dimensional Space

In this work, we proposed ultra generalized exponential–hyperbolic potential (UGEHP) and derived various well known exponential–hyperbolic type potentials by setting parameters in UGEHP and using approximation suggested by Greene–Aldrich. The bound state solutions of the multi (D)-dimensional Schrodinger equation for UGEHP have been presented using the parametric Nikiforov–Uvarov method. The approximate analytical bound state energy eigenvalues and the corresponding un-normalized eigenfunctions expressed in terms of hypergeometric functions were obtained. We also investigated the rotational vibrational (RV) partition function from the eigenvalue of UGEHP. By the setting parameters, we obtained eigenvalue spectrum and RV partition function for the screened cosine Kratzer potential, screened Kratzer potential, attractive radial potential, quadratic exponential-type potential, Manning Rosen with class of Yukawa potential and Yukawa potential, class of Yukawa potential, mixed class of Yukawa potential, quantum interaction potential or Hulthen–Yukawa inversely quadratic potential, Hulthen plus inversely quadratic exponential Mie-type potential and Hulthen plus exponential Coulombic potential with centrifugal potential barrier. We studied the behavior of energy eigenvalues and RV partition function for the UGEHP. We computed and tabulated numerical results for $$CO, NO, I_2$$ , HCl and LiH diatomic molecules and compared with numerical results available in literature for same diatomic molecules.

Theoretical prediction of thermodynamic properties of N2 and CO using pseudo harmonic and Mie-type potentials

In this work, thermodynamic properties of nitrogen (N2) and carbon monoxide (CO) were theoretically predicted by using two potential models, pseudo harmonic and Mie-type. We have solved the Schrödinger equation for the potential models and obtained the analytical expressions for energy eigenvalues. Using the energy spectra, partition function and thermodynamic properties of N2 and CO were calculated. Examples of the thermodynamic properties are specific heat at constant pressure, entropy and enthalpy. According to the obtained results, it is found that there is good agreement between our theoretical results and experimental data.

Collective depinning of driven monolayer active colloidal particles with magnetic dipole and Mie-type interactions

We report Langevin simulations on the collective depinning of driven monolayer active colloidal particles over the disordered substrate. The active colloidal particles are modeled as Janus particles interacting with magnetic dipole and Mie-type potentials. On increasing the Mie-type potential exponent , we find a peak of critical pinning force at . Above the depinning, there are living islands when the exponent is less than , and they disappear once is larger than . Further increasing the exponent will lead to moving crystal structures above the depinning. Moreover, the peak of critical pinning force occurs at a weaker strength of magnetic-dipole interaction as is increased to be a larger value, and it disappears as is further increased over . Finally, the critical pinning force remains basically unchanged with the strength of Mie-type potential, except for the system of , where the critical pinning force decreases with the strength of Mie-type potential. Our results are helpful to understand the formation of self-organisation in electromagnetic interaction biological systems driven by external field.

Solutions of Klein–Gordon equation with Mie-type potential via the Laplace transforms

A study is undertaken to derive the exact solutions of the Klein–Gordon with the Mie-type potential in the presence of the nonzero space component of a vector potential field. The wave functions and the energy spectrum are derived via the Laplace transformation method and by assuming equal scalar and time component of the vector potential. The Mie-type potential describes four different types of potential at the same time. The energy spectrum separately is obtained for each potential, and an estimation of the most general case is introduced.

Time independent fractional Schrödinger equation for generalized Mie-type potential in higher dimension framed with Jumarie type fractional derivative

In this paper, we obtain approximate bound state solutions of an N-dimensional fractional time independent Schrödinger equation for a generalised Mie-type potential, namely, V(rα)=Ar2α+Brα+C. Here α(0 < α < 1) acts like a fractional parameter for the space variable r. When α = 1 the potential converts into the original form of Mie-type of potential that is generally studied in molecular and chemical physics. The entire study is composed with a Jumarie-type fractional derivative approach. The solution is expressed via the Mittag-Leffler function and fractionally defined confluent hypergeometric function. To ensure the validity of the present work, obtained results are verified with the previous studies for different potential parameter configurations, specially for α = 1. At the end, few numerical calculations for energy eigenvalue and bound state eigenfunctions are furnished for a typical diatomic molecule.

A study of ∇-discrete fractional calculus operator on the radial Schrödinger equation for some physical potentials

The fractional calculus includes concepts of integrals and derivatives of any complex or real order. The fractional calculus is as old as the usual calculus. Recently, many scientists have been studying on this field to provide the development and applicability to various areas of mathematics, physics, engineering and other sciences. The discrete fractional calculus has an important position in this field. Some ordinary diffrential equations can be solved by means of nabla (∇) discrete fractional calculus operator. In this paper, we aim to apply this operator to the radial Schrödinger equation for some physical potentials such as pseudoharmonic and Mie-type potentials.

Semiflexible polymers confined in a slit pore with attractive walls: two-dimensional liquid crystalline order versus capillary nematization.

Semiflexible polymers under good solvent conditions interacting with attractive planar surfaces are investigated by Molecular Dynamics (MD) simulations and classical Density Functional Theory (DFT). A bead-spring type potential complemented by a bending potential is used, allowing variation of chain stiffness from completely flexible coils to rod-like polymers whose persistence length by far exceeds their contour length. Solvent is only implicitly included, monomer-monomer interactions being purely repulsive, while two types of attractive wall-monomer interactions are considered: (i) a strongly attractive Mie-type potential, appropriate for a strictly structureless wall, and (ii) a corrugated wall formed by Lennard-Jones particles arranged on a square lattice. It is found that in dilute solutions the former case leads to the formation of a strongly adsorbed surface layer, and the profile of density and orientational order in the z-direction perpendicular to the wall is predicted by DFT in nice agreement with MD. While for very low bulk densities a Kosterlitz-Thouless type transition from the isotropic phase to a phase with power-law decay of nematic correlations is suggested to occur in the strongly adsorbed layer, for larger densities a smectic-C phase in the surface layer is detected. No "capillary nematization" effect at higher bulk densities is found in this system, unlike systems with repulsive walls. This finding is attributed to the reduction of the bulk density (in the center of the slit pore) due to polymer adsorption on the attractive wall, for a system studied in the canonical ensemble. Consequently in a system with two attractive walls nematic order in the slit pore can occur only at a higher density than for a bulk system.

Equilibrium molecular theory of two-dimensional adsorbate drops on surfaces of heterogeneous adsorbents

A molecular statistical theory for calculating the linear tension of small multicomponent droplets in two-dimensional adsorption systems is developed. The theory describes discrete distributions of molecules in space (on a scale comparable to molecular size) and continuous distributions of molecules (at short distances inside cells) in their translational and vibrational motions. Pair intermolecular interaction potentials (the Mie type potential) in several coordination spheres are considered. For simplicity, it is assumed that distinctions in the sizes of mixture components are slight and comparable to the sizes of adsorbent adsorption centers. Expressions for the pressure tensor components inside small droplets on the heterogeneous surface of an adsorbent are obtained, allowing calculations of the thermodynamic characteristics of a vapor–fluid interface, including linear tension. Problems in refining the molecular theory are discussed: describing the properties of small droplets using a coordination model of their structure, considering the effect an adsorbate has on the state of a near-surface adsorbent region, and the surface heterogeneity factor in the conditions for the formation of droplets.

A New Relativistic Study for Interactions in One-electron atoms (Spin ½ Particles) with Modified Mie-type Potential

A New Relativistic Study for Interactions in One-electron atoms (Spin ½ Particles) with Modified Mie-type Potential

Mie-type potential from a class of multiparameter exponential-type potential: Bound state solutions in D dimensions

The Mie potential is a model of molecular interaction, very useful in the study of diatomic molecules because allows one to describe the softness/hardness of the repulsive interactions as well as the range of attraction. As a consequence, the Mie potential and one of their particular cases, the Lennard-Jones potential, have been extensively used in many branches of physics and chemistry. In this work, the exact bound state solutions of the D-dimensional Schrödinger equation with the Mie-type potential are presented. These eigen-functions/values are obtained as a particular case of the exactly solvable Schrödinger equation for a class of multiparameter exponential-type potential. Furthermore our approach does not need any approximation to the centrifugal term. As an example of the usefulness of our proposition, we show how the bound state solutions of the Kratzer-Fues and Coulomb potentials in D-dimensions are particular cases from the proposal.

Analysis of quantum-mechanical states of the ring-shaped Mie-type diatomic molecular model via the Fisher's information

Recently, the information theory of quantum-mechanical systems has aroused the interest of many theoretical physicists. This is due to the fact that it provides a deeper insight into the internal structure of the system. Also, it is the strongest support of the modern quantum computation and information, which is a basic theory for numerous technological developments. This study reports the solution of Schrödinger equation with the ring-shaped Mie-type potential. The rotational-vibrational spectroscopic study of some few selected diatomic molecules are given. The probability distribution density of the system which gives the probability density for observing the electron in the state characterized by the quantum numbers (n, l, m) in the ring-shaped Mie-type potential is obtained. Finally, the analysis for this distribution via a complementary information measures of a probability distribution known as the Fisher's information have been presented.

A Laplace transform approach to find the exact solution of the $$N$$ N -dimensional Schrödinger equation with Mie-type potentials and construction of Ladder operators

The second order N-dimensional Schrodinger equation with Mie-type potentials is reduced to a first order differential equation by using the Laplace transformation. Exact bound state solutions are obtained using convolution or Faltungs theorem. The Ladder operators are also constructed for the Mie-type potentials in N- dimensions. Lie algebra associated with these operators are studied and it is found that they satisfy the commutation relations for the SU(1,1) group.

Relativistic effect of pseudospin symmetry and tensor coupling on the Mie-type potential via Laplace transformation method

A relativistic Mie-type potential for spin-1/2 particles is studied. The Dirac Hamiltonian contains a scalar S(r) and a vector V(r) Mie-type potential in the radial coordinates, as well as a tensor potential U(r) in the form of Coulomb potential. In the pseudospin (p-spin) symmetry setting Σ = Cps and Δ = V(r), an analytical solution for exact bound states of the corresponding Dirac equation is found. The eigenenergies and normalized wave functions are presented and particular cases are discussed with any arbitrary spin—orbit coupling number κ. Special attention is devoted to the case Σ = 0 for which p-spin symmetry is exact. The Laplace transform approach (LTA) is used in our calculations. Some numerical results are obtained and compared with those of other methods.