Exponential-type Potential Research Articles

Quantum information-entropic measures for exponential-type potential

The approximate solutions of the Schrödinger equation with the central generalized Hulthén and Yukawa potential are investigated within the framework of the functional method. The obtained wave function and the energy levels are used to study the Shannon entropy, Renyi entropy, Fisher information, Shannon Fisher complexity, Shannon power and Fisher-Shannon product in both position and momentum spaces for the ground and first excited states. The theoretic information theories such as Shannon entropies Sr,Sp, Fisher information Ip,Ip and Renyi entropies Rβ as well as the information entropy probability densities ρ(r),ϕ(p) are illustrated graphically. The Bialynicki-Birula – Mycielski (BBM) inequality for the Shannon entropies and the Cramer-Rao inequality for the Fisher information are satisfied for the potential model.

Computing thermodynamic properties of the O2 and H2 molecules with multi-parameter exponential-type potential

In this paper, we determine the vibrational partition function using improved energy spectrum obtained recently via the path integral formalism. Based on that, we compute the thermodynamic properties of the O2 and H2 molecules, for a multi-parameter exponential-type potential describing the internal vibration. We validate our results on the molecular entropy; the calculated values and the experimental data are in excellent agreement.

Thermodynamic properties of improved deformed exponential-type potential (IDEP) for some diatomic molecules

Within the framework of non-relativistic quantum mechanics, the ro-vibrational energy spectra of the improved deformed exponential-type potential model are obtained using the Greene-Aldrich approximation scheme and an appropriate coordinate transformation. With the help of the energy spectra, analytical expressions of the vibrational partition function and other thermodynamic functions are derived by employing the Poisson summation formula. These thermodynamic functions are studied for the electronic states of hydrogen dimer, carbon monoxide, nitrogen dimer and lithium hydride diatomic molecules, as they vary with temperature and upper bound vibration quantum number.

Approximate ℓ‐bound state solutions of q‐deformed exponential‐type potentials

AbstractIn this work, the exactly solvable Schrödinger equation for s‐states of a class of multiparameter exponential‐type potential (E‐tP) is used to obtain the approximate ℓ ≠ 0 bound state solutions for the corresponding q‐deformed radial potentials. To deal with the effective potential, the Pekeris approximation for the centrifugal term is applied. The proposal has the advantage that, depending on the choice of the parameters involved in the E‐tP, several q‐deformed exponential potentials are obtained here as particular cases. That is, our proposition indicates that it is not necessary to use specialized methods to solve the Schrödinger equation for specific q‐deformed exponential potentials. At this regard, in order to show the usefulness of the proposed method, we consider the ℓ ≠ 0 bound state solutions of the q‐deformed Tietz, Hulthén, Manning‐Rosen, Shioberg, quadratic exponential, Wei and Hua among other potential models. Furthermore, with the example of the Hua potential we are contributing to solve the recent controversy on the energy spectra of this q‐deformed model. Moreover, in some applications considered in this work the results can be used to correct similar findings already published. Besides, the proposal is useful when considering new q‐deformed potentials with hypergeometric wavefunctions to be used in quantum chemical applications of diatomic molecules.

Thermodynamic functions for boron nitride with q-deformed exponential-type potential

Within the framework of the supersymmetric quantum mechanics, the energy spectrum of the six-parameter exponential-type potential model was obtained. The partition function for this energy has been calculated in a closed and compact form and was used to obtain an expression for the ro-vibrational mean free energy F(T), mean free energy U(T), entropy S(T), and the specific heat capacity C(T). The thermodynamic functions obtained were then applied to study the behaviour of the zinc-blende BN crystal structure and the results obtained show fair agreement with reported experimental data for the specific heat capacity.

Feinberg-Horodecki Exact Momentum States of Improved Deformed Exponential-Type Potential

We obtain the quantized momentum eigenvalues, Pn, and the momentum eigenstates for the space-like Schrodinger equation, the Feinberg-Horodecki equation, with the improved deformed exponential-type potential which is constructed by temporal counterpart of the spatial form of these potentials. We also plot the variations of the improved deformed exponential-type potential with its momentum eigenvalues for few quantized states against the screening parameter.

Bohr Hamiltonian with multiparameter exponential-type potential for triaxial nuclei

The Bohr Hamiltonian with multiparameter exponential-type potential for the \( \beta\)-part and a harmonic oscillator for the \( \gamma\)-part is solved. The \( \beta\)-part has been solved using the Nikoforov-Uvarov method. The wave function and energy expression has been derived. The electric quadrupole transition rates are evaluated. The numerical results for energy spectra and B(E2)’s are compared to the experimental data of 192, 194, 196Pt atomic nuclei and there is an overall good agreement.

Position-dependent mass Schrödinger equation for exponential-type potentials.

In quantum chemical calculations, there are two facts of particular relevance: the position-dependent mass Schrödinger equation (PDMSE) and the exponential-type potentials used in the theoretical study of vibrational properties for diatomic molecules. Accordingly, in this work, the treatment of exactly solvable PDMSE for exponential-type potentials is presented. The proposal is based on the exactly solvable constant mass Schrödinger equation (CMSE) for a class of multiparameter exponential-type potentials, adapted to the position-dependent-mass (PDM) kinetic energy operator in the O von Roos formulation. As a useful application, we consider a PDM distribution of the form [Formula: see text], where the different parameters can be adjusted depending on the potential under study. The principal advantage of the method is that solution of different specific PDM exponential potential models are obtained as particular cases from the proposal by means of a simple choice of the involved exponential parameters. This means that is not necessary resort to specialized methods for solving second-order differential equations as usually done for each specific potential. Also, the usefulness of our results is shown with the calculation of s-waves scattering cross-section for the Hulthén potential although this kind of study can be extended to other specific potential models such as PDM deformed potentials.

Analytical solution of the Feynman Kernel for general exponential-type potentials

This paper presents an analytical path-integral treatment of the ℓ-states of an exponential-type potential. We propose a generalization of the Pekeris approximation of the centrifugal term adapted to deformed potentials. To obtain solutions of the radial Feynman Kernel for arbitrary angular number, we perform a nontrivial change of variable accompanied by a local time rescaling. Using Euler angles and the isomorphism between S3 and SU(2), we convert the radial path integral into a maniable one. Analytical expressions of the energy spectrum and the normalized ℓ-state eigenfunctions are derived from the Green function. Several potentials are obtained as special cases of the general exponential-type potential. Thus, their eigenvalues and eigenfunctions are deduced straightforwardly. Numerical results show that our technique improves the state-of-the-art.

Improved Five-Parameter Exponential-Type Potential Energy Model for Diatomic Molecules**Supported by the National Natural Science Foundation of China under Grant No. 10675097 and the Sichuan Province Foundation of China for Fundamental Research Projects under Grant No. 2018JY0468

The dissociation energy and equilibrium bond length as explicit parameters are used to establish an improved five-parameter exponential-type potential energy model for diatomic molecules. We demonstrate that the five-parameter exponential-type potential is identical to the Tietz potential for diatomic molecules. It is observed that the improved five-parameter exponential-type potential can well model the internuclear interaction potential energy curve for the ground electronic state of the carbon monoxide molecule by the utilization of the experimental values of three molecular constants.

Generalized Dirac Oscillator in Cosmic String Space-Time

In this work, the generalized Dirac oscillator in cosmic string space-time is studied by replacing the momentum pμ with its alternative pμ+mωβfμxμ. In particular, the quantum dynamics is considered for the function fμxμ to be taken as Cornell potential, exponential-type potential, and singular potential. For Cornell potential and exponential-type potential, the corresponding radial equations can be mapped into the confluent hypergeometric equation and hypergeometric equation separately. The corresponding eigenfunctions can be represented as confluent hypergeometric function and hypergeometric function. The equations satisfied by the exact energy spectrum have been found. For singular potential, the wave function and energy eigenvalue are given exactly by power series method.

A study of thermodynamic properties of quadratic exponential-type potential in D-dimensions

We solved the Schrodinger equation with Quadratic Exponential-Type Potential (QEP) model in D-dimensions using the Modified factorization method. The energy eigenvalues and total wavefunctions were obtained in a Gauss hypergeometric form. The thermodynamic properties including vibrational partition function, vibrational mean energy, vibrational mean free energy and vibrational entropy have been calculated for the electronic state of (X1 Σ +g) Rubidium (Rb2) dimer. The QEP discussed can be applied extensively in Physics and Chemistry, especially in molecular dynamics.

Information-theoretic measure of the hyperbolical exponential-type potential

The approximate analytical solution of the 3-dimensional radial Schrödinger equation in the framework of the parametric Nikiforov-Uvarov method was obtained with a hyperbolical exponential-type potential. The energy eigenvalue equation and the corresponding wave function have been obtained explicitly. Using the integral method, we calculated Shannon entropy, information energy, Fisher information, and complexity measure. It was deduced that the complexity measure calculated using Shannon entropy with information energy and that calculated using Shannon entropy with Fisher information were similar.

On the q-deformed exponential-type potentials

In this work, both non-deformed and q-deformed exactly solvable multiparameter exponential-type potentials $$V^{\pm }(r)$$ are obtained; $$V^{+}(r=x)$$ stands for one-dimensional potential and $$V^{-}(r)$$ for the radial part of s-states used in the treatment of vibrational properties of diatomic molecules. As a first result, we show that non-deformed potentials arise from non-q-dependent parameters involved in $$V^{\pm }(r)$$ and rather correspond to a class of q-shifted exponential-type potentials obtained from the Arai’s q-deformed hyperbolic functions. As a second result, by using q-dependent parameters in $$V^{\pm }(r)$$ it is possible to obtain true q-deformed exponential-type potentials. As a useful application of these potentials, some examples of q-deformed exponential-type potentials are considered by means of a proper selection of the involved parameters. Our proposal is general and can be viewed as a unified treatment to the study of q-deformed exponential-type potentials with the advantage that it is not necessary to use a specialized method for solving the Schrodinger equation to each specific potential because many of them are obtained as particular cases of $$V^{\pm }(r)$$ . Furthermore, new q-deformed potentials used as interesting alternatives in quantum chemical applications can be derived.

Analysis of minimal length effect on the non-relativistic energy and wave function for the exponential type potential using Supersymmetric Quantum Mechanics

In this research, the minimal length effect was analysed on the energy and wave functions of the non-relativistic mechanical quantum system by studying the Schrodinger equation. The three dimensional Schrodinger equation with minimal length for the exponential type potential was solved by using supersymmetric quantum mechanics. To get the solution, the exponential type potential was reduced to the Morse potential. The non-relativistic energy was calculated numerically for diatomic molecules, LiH and HCl by using the Matlab software. From the results were shown that the presence of minimal length gives effect to the non-relativistic energy, it was seen clearly in the higher value of angular momentum l and quantum number n.

Primordial perturbations from inflation with a hyperbolic field-space

We study primordial perturbations from hyperinflation, proposed recently and based on a hyperbolic field-space. In the previous work, it was shown that the field-space angular momentum supported by the negative curvature modifies the background dynamics and enhances fluctuations of the scalar fields qualitatively, assuming that the inflationary background is almost de Sitter. In this work, we confirm and extend the analysis based on the standard approach of cosmological perturbation in multifield inflation. At the background level, to quantify the deviation from de Sitter, we introduce the slow-varying parameters and show that steep potentials, which usually cannot drive inflation, can drive inflation. At the linear perturbation level, we obtain the power spectrum of primordial curvature perturbation and express the spectral tilt and running in terms of the slow-varying parameters. We show that hyperinflation with power-law type potentials has already been excluded by the recent Planck observations, while exponential-type potential with the exponent of order unity can be made consistent with observations as far as the power spectrum is concerned. We also argue that, in the context of a simple $D$-brane inflation, the hyperinflation requires exponentially large hyperbolic extra dimensions but that masses of Kaluza-Klein gravitons can be kept relatively heavy.

Analytic Spin and Pseudospin Solutions to the Dirac Equation for the Quadratic Exponential-Type Potential Plus Eckart Potential and Yukawa-Like Tensor Interaction

We solve the Dirac equation for the quadratic exponential-type potential plus Eckart potential including a Yukawa-like tensor potential with arbitrary spin–orbit coupling quantum number κ. In the framework of the spin and pseudospin (pspin) symmetry, we obtain the energy eigenvalue equation and the corresponding eigenfunctions in closed form by using the Nikiforov–Uvarov method. Also Special cases of the potential as been considered and their energy eigen values as well as their corresponding eigen functions are obtained for both relativistic and non-relativistic scope.

Non-deformed singular and non-singular exponential-type potentials

The canonical transformation method applied to the Schrödinger equation to transform it into a second-order differential equation of hypergeometric-type is presented. Starting from there, those exactly solvable multiparameter exponential-type (ME-T) potentials with hypergeometric wavefunctions that belong to the families of radial (singular) and one-dimensional (non-singular) potentials, are obtained. Furthermore, we show how the choice of the involved parameters leads, as particular cases, to different deformed or non-deformed potential models already used in the study of electronic properties of diatomic molecules. Also, the analysis of parameters lets us identify the couple of potential partners (singular/non-singular) that correspond to each choice of the parameters appearing in the ME-T potential. As a useful application of the proposal, the most important non-deformed exponential potential models are considered for which it can be viewed as a unified treatment with the following advantages: (1) It is not necessary to use a special method to solve the Schrödinger equation for a specific potential model because solution is obtained as particular case by the simple choice of the involved parameters; (2) The families of singular and non-singular potentials are straightforward identified; (3) The corresponding associated partners, between radial and one-dimensional non-deformed potentials, are found; (4) New potentials, as interesting alternatives for quantum applications, are obtained. In addition, from the conditions that parameters must meet to have physically acceptable solutions, we establish the requirements for the existence or not of singular/non-singular potential partners.

Bound state solutions of Dirac equation with radial exponential-type potentials

In this work, a direct approach for obtaining analytical bound state solutions of the Dirac equation for radial exponential-type potentials with spin and pseudospin symmetry conditions within the frame of the Green and Aldrich approximation to the centrifugal term is presented. The proposal is based on the relation existing between the Dirac equation and the exactly solvable Schrödinger equation for a class of multi-parameter exponential-type potential. The usefulness of the present approach is exemplified by considering some known specific exponential-type potentials which are obtained as particular cases from our proposal. That is, instead of solving the Dirac equation for a special exponential potential, by means of a specialized method, the energy spectra and wave functions are derived directly from the proposed approach. Beyond the applications considered in this work, our proposition could be used as an alternative way in the search of bound state solutions of the Dirac equation for other potentials as well as it can be easily adapted to other approximations to the centrifugal term.

Position-Dependent Mass Schrödinger Equation for the Morse Potential

The position dependent mass Schrödinger equation (PDMSE) has a wide range of quantum applications such as the study of semiconductors, quantum wells, quantum dots and impurities in crystals, among many others. On the other hand, the Morse potential is one of the most important potential models used to study the electronic properties of diatomic molecules. In this work, the solution of the effective mass one-dimensional Schrödinger equation for the Morse potential is presented. This is done by means of the canonical transformation method in algebraic form. The PDMSE is solved for any model of the proposed kinetic energy operators as for example the BenDaniel-Duke, Gora-Williams, Zhu-Kroemer or Li-Kuhn. Also, in order to solve the PDMSE with Morse potential, we consider a superpotential leading to a special form of the exactly solvable Schrödinger equation of constant mass for a class of multiparameter exponential-type potential along with a proper mass distribution. The proposed approach is general and can be applied in the search of new potentials suitable on science of materials by looking into the viable choices of the mass function.