Pseudoharmonic Potential Research Articles

Fisher Information for a System Composed of a Combination of Similar Potential Models

The solutions to the radial Schrödinger equation for a pseudoharmonic potential and Kratzer potential have been studied separately in the past. Despite different reports on the Kratzer potential, the fundamental theoretical quantities such as Fisher information have not been reported. In this study, we obtain the solution to the radial Schrödinger equation for the combination of the pseudoharmonic and Kratzer potentials in the presence of a constant-dependent potential, utilizing the concepts and formalism of the supersymmetric and shape invariance approach. The position expectation value and momentum expectation value are calculated employing the Hellmann–Feynman Theory. These expectation values are then used to calculate the Fisher information for both position and momentum spaces in both the absence and presence of the constant-dependent potential. The results obtained revealed that the presence of the constant-dependent potential leads to an increase in the energy eigenvalue, as well as in the position and momentum expectation values. Additionally, the constant-dependent potential increases the Fisher information for both position and momentum spaces. Furthermore, the product of the position expectation value and the momentum expectation value, along with the product of the Fisher information, satisfies both Fisher’s inequality and Cramer–Rao’s inequality.

Effects of Topological Defects and AB Fields on the Thermal Properties, Persistent Currents and Energy Spectra with an Exponential-Type Pseudoharmonic Potential

Effects of Topological Defects and AB Fields on the Thermal Properties, Persistent Currents and Energy Spectra with an Exponential-Type Pseudoharmonic Potential

Electrostatics of soft (bio)interfaces: Corrections of mean-field Poisson-Boltzmann theory for ion size, dielectric decrement and ion-ion correlations

HypothesisElectrostatics of soft (ion-permeable) (bio)particles (e.g. microorganisms, core/shell colloids) in aqueous electrolytes is commonly formulated by the mean-field Poisson-Boltzmann theory and integration of the charge contributions from electrolyte ions and soft material. However, the effects connected to the size of the electrolyte ions and that of the structural charges carried by the particle, to dielectric decrement and ion-ion correlations on soft interface electrostatics have been so far considered at the margin, despite the limits of the Gouy theory for condensed and/or multivalent electrolytes. ExperimentsAccordingly, we modify herein the Poisson-Boltzmann theory for core/shell (bio)interfaces to include the aforementioned molecular effects considered separately or concomitantly. The formalism is applicable for poorly to highly charged particles in the thin electric double layer regime and to unsymmetrical multivalent electrolytes. FindingsComputational examples of practical interests are discussed with emphasis on how each considered molecular effect or combination thereof affects the interfacial potential distribution depending on size and valence of cations and anions, size of particle charges, length scale of ionic correlations and shell-to-Debye layer thickness ratio. The origins of here-evidenced pseudo-harmonic potential profile and ion size-dependent screening of core/shell particle charges are detailed. In addition, the existence and magnitude of the Donnan potential when reached in the shell layer are shown to depend on the excluded volumes of the electrolyte ions.

Mass spectra and thermal properties of deformed Schrödinger Equation for pseudoharmonic potential

In this research, non-relativistic Schrödinger Equation was solved and the related quantum mechanical properties were solved using the Nikiforov–Uvarov (NU) method. The energy spectrum and wave function of the pseudoharmonic potential model are obtained. We applied the energy eigenvalues to investigate the mass spectra (MS) of heavy mesons such as charmonium and bottomonium. In addition, the partition function is calculated in a closedform and is used to obtain expressions for other thermal properties such as vibrational free energy, mean energy, vibrational entropy, and vibrational heat capacity. The MS was found to be in agreement with the experimental data and previously reported results of others.

Relativistic bound states of the pseudoharmonic potential in the presence of external magnetic and Aharonov–Bohm fields

Relativistic bound states of the pseudoharmonic potential in the presence of external magnetic and Aharonov–Bohm fields

Dielectric effect on the optical properties of exciton quantum dot with Gaussian plus generalized Hulthen potential as Pseudo-Harmonic potential

The dielectric effect on the intersubband optical properties for a core/shell quantum dots system is investigated with the Gaussian plus generalized Hulthen potential as a Pseudo-Harmonic potential model. The analytical solutions of the bound states energy and eigenfunctions were calculated using the Nikiforov–Uvarov (N–U). A detailed investigation of the linear dielectric function, third-order nonlinear dielectric function, total absorptions coefficient, and the transmission coefficient has been examined using the density matrix formalisms. Our result reveals that the dielectric constant affects the core materials and enhances the spectra shift, while the shell materials for both materials examined remains constant at zero photon-energy levels.

Fisher information of a vector potential for time‐dependent Feinberg–Horodecki equation

AbstractThe time‐dependent Feinberg–Horodecki equation in the presence of a special Mie‐type pseudoharmonic potential was solved and the quantized momentum with the corresponding wave functions were obtained with the supersymmetric approach. The Fisher information for both the time and the momentum space were calculated via expectation values of time and momentum. The effect of the dissociation energy, the equilibrium time point and the quantum number respectively on the Fisher information were studied in detail. The result was applied to five molecules. The results obtained for the time‐dependent Feinberg–Horodecki equation followed the trend of the results obtained for the time‐independent Schrödinger equation.

Lorentz violation induced by Rashba coupling via non-commutative geometry

In this paper we consider a simple non-relativistic quantum system for a particle confined inside a pseudo-harmonic oscillator potential in the non-commutative space. We study the influence of non-commutative background on the energy spectrum of the particle by considering the Rashba spin-orbit interaction. We show that the Rashba interaction can generate the Lorentz violation effect in the non-commutative background, which is independent of potential. Finally, we find a compatible bound on the Lorentz violation parameter of electrons as an order of in the non-relativistic system.

Analytic solutions for vibrational energy levels of the pseudoharmonic potential

The non-relativistic analytic solutions of a quantum mechanical system have been calculated for the case of pseudoharmonic potential by using the Whittaker functions approach. A diatomic quantum system is placed in a Pseudoharmonic potential and perturbed by an external magnetic field. The resulting Schrodinger’s equation has been solved exactly to obtain the analytic expressions of vibrational energy levels and associated wave functions. In this work, we have compared the results of six diatomic molecules with those available in the literature.

The Optical Polaron Effect on the Coherent Time of a qubit in the RbCl Quantum Dot with Two-Dimensional Pseudoharmonic Potential

The effects of optical polarons on qubit coherence times in a RbCl quantum dot (QD) under a pseudoharmonic potential (PHP) are theoretically investigated using Fermi’s Golden Rule and Pekar type variational method (PTVM). From this, coherence time variations are analytically driven as a function of the chemical potential (CP) of two-dimensional electron gas (2DEG), polaron radius and PHP zero point, which are shown to have a significant impact. Our results provide a theoretical method for solving stability issues with qubits during quantum information.

WKB Energy Expression for the Radial Schrödinger Equation with a Generalized Pseudoharmonic Potential

In this paper, we applied the semi-classical quantization approximation method to solve the radial Schrödinger equation with a generalized Pseudoharmonic potential. The four turning points problem within the framework of the Wentzel-Kramers-Brillouin (WKB) method was transformed into two turning points and subsequently, the energy spectrum was obtained. Some special cases of the generalized Pseudoharmonic potential are presented. The WKB approximation approach reproduces the exact energy expression obtained with several analytical methods in the literature. The values of the energy levels for some selected diatomic molecules (N2, CO, NO, CH) obtained numerically are in excellent agreement with those from previous works in the literature.

Superstatistics of Schrödinger equation with pseudo-harmonic potential in external magnetic and Aharanov-Bohm fields

In this work, the thermodynamic properties of pseudo-harmonic potential in the presence of external magnetic and Aharanov-Bohm fields are investigated. The effective Boltzmann factor in the superstatistics formalism was used to obtain the thermodynamic properties such as Helmholtz free energy, Internal energy, entropy and specific heat capacity of the system. In addition, the thermal properties of some selected diatomic molecules of N2,Cl2,I2 and CH using their experimental spectroscopic parameters and the effect of varying the deformation parameter of q=0,0.3,0.7 were duly examined.

Exact solutions and spectrum analysis of a noncentral potential in the presence of vector potential

AbstractWe studied exact solutions and spectrum analysis of the pseudoharmonic oscillator in the presence of θ‐dependent scalar potential and the sum of two vector potentials Dirac magnetic monopole and Aharonov‐Bohm field. The effect of the Dirac magnetic monopole (g), Aharonov‐Bohm field (ℱ), the dissociation energy of diatomic molecules (D e), equilibrium intermolecular separation (r e), and the reduced mass (μ) on the energy spectrum for some diatomic molecules (CO, NO, N2, CH, H2, and ScH) are analyzed. We compared our results with theoretical experiments of pseudoharmonic oscillator potential in a molecular system.

Higher-dimensional fractional time-independent Schrödinger equation via fractional derivative with generalised pseudoharmonic potential

In this paper, we obtain approximate bound-state solutions of N-dimensional time-independent fractional Schrodinger equation for the generalised pseudoharmonic potential which has the form $$V(r^{\alpha })=a_1r^{2\alpha } + ({a_2}/{r^{2\alpha }})+a_3$$ . Here $$\alpha \;(0<\alpha <1)$$ acts like a fractional parameter for the space variable r. The entire study consists of the Jumarie-type fractional derivative and the elegance of Laplace transform. As a result, we can successfully express the approximate bound-state solution in terms of Mittag–Leffler function and fractionally defined confluent hypergeometric function. Our study may be treated as a generalisation of all previous works carried out on this topic when $$\alpha =1$$ and N arbitrary. We provide numerical result of energy eigenvalues and eigenfunctions for a typical diatomic molecule for different $$\alpha $$ close to unity. Finally, we try to correlate our work with a Cornell potential model which corresponds to $$\alpha = {1}$$ $$/$$ $${2}$$ with $$a_3=0$$ and predicts the approximate mass spectra of quarkonia.

The Effects of Electric Field on the Coherence Time of RbCl Quantum Pseudodot Qubit

We academically explore the properties of the coherence time (CT) of an electron powerful coupled to the phonons in a RbCl quantum pseudodot (QPD) qubit with an exterior electric field alongside the ρx direction. By employing the Pekar type variational method (PTVM) and the Fermi golden rule, the CT changes with the electric field, the chemical potential of the two-dimensional electron gas (CPTDEG), the zero point of the pseudoharmonic potential (ZPPHP) and the polaron radius is studied. The examined results indicate ① that the CT of RbCl QPD qubit decays with aggrandizing electric field, ② that the CT is a decreasing function of the CPTDEG, the ZPPHP and the polaron radius, ③ that here we can find that we can adjust the CT by changing the external electric field, the CPTDEG, the ZPPHP and the polaron radius.

Two-Electron Pseudodot System With Laser Effect in Plasmas

We have studied the two-electron pseudodot (TEPD) system immersed in plasma environments under the influence of a monochromatic linearly polarized laser field. The four different sets, constituted by the potential parameters, of the more general exponential cosine screened Coulomb potential are used to characterize the Debye and quantum plasma environments. The time dependent in the Schrodinger equation arising from the laser field is interchanged to the potential energy term from the kinetic energy term through the dipole approximation and the Kramers–Henneberger transformation. Then, the laser-dressed potential that denotes the effects of the laser radiation field is constituted by using the Ehlotzky approximation. In that case, as the analytical solution is impossible just now due to the complicated form of the Schrodinger equation, the numerical solution is carried out via the asymptotic iteration method. In this paper, the pseudodot system is considered because the quantum dots are very similar to atomic systems, and the pseudoharmonic potential is successful in explaining the atomistic structures. However, it is an important motivation for us that, as well as the importance of the laser–plasma interactions, the laser field is a considerable exciter for radiating, which exhibits remarkable confinement effects. Since, as well as the screening effects exhibited by plasmas on atomic systems, and their significant results, the plasma is a significant experimental argument in manufacturing and modification of the quantum dots, the plasma effects are taken into consideration in this paper. Within these motivations, all parameters that operate on the energies of TEPD system with the laser effect in plasmas are analyzed in detail, and the corresponding results are discussed thoroughly.

The magnetic field effect on the coherence time of qubit in RbCl crystal quantum pseudodot

In an external z-direction magnetic field, the coherence property of qubit in RbCl crystal quantum pseudodot (QPD) is discussed. The coherence time of QPD qubit is calculated by using the Pekar type variational method and the Fermi Golden Rule. It is analytically derived that the coherence time versus the cyclotron frequency of the magnetic field and the QPD parameters (the chemical potential of the two-dimensional electron gas, the zero point of pseudoharmonic potential, and the polaron radius) in QPD system. According to the results, it is found that the parameters and the magnetic field adjusts the coherence time of the qubit in the RbCl crystal QPD.

The Effect of Coulomb Impurity Potential on the Coherence Time of RbCl Quantum Pseudodot Qubit

We have considered the pseudoharmonic potential (PHP) for a RbCl quantum pseudodot (QPD) qubit with a hydrogen-like impurity at the center. By employing the Pekar variational method and the Fermi Golden Rule, we study the properties of the coherence time of an electron strongly interacting with longitudinal optical phonon in a RbCl QPD qubit. The coherence time changing with the Coulombic impurity potential strength, the two-dimensional chemical potential of the electron gas, the PHP zero point and the polaron radius is theoretically investigated. The obtained results indicate that ① the coherence time of RbCl QPD qubit decreases with increasing Coulombic impurity potential strength, ② the coherence time is a decaying function of the two-dimensional chemical potential of the electron gas and the PHP zero point, ③ the smaller the polaron radius is, the smaller the coherence time is.

Solutions of Two-dimensional Schrodinger Equation in Symmetries of Extended Quantum Mechanics for the Modified Pseudoharmonic Potential: an Application to Some Diatomic Molecules

Solutions of Two-dimensional Schrodinger Equation in Symmetries of Extended Quantum Mechanics for the Modified Pseudoharmonic Potential: an Application to Some Diatomic Molecules

Temperature Effects on the First Excited State of the Polaron in an Asymmetric Quantum Pseudodot Under Magnetic Field

Using the variational method of the Pekar type, we investigate the first excited state energy of the polaron in an asymmetric quantum pseudodot under the magnetic field. Temperature effects on the polaron are calculated by employing the quantum statistical theory, and the influences of the chemical potential, the zero point of pseudo-harmonic potential (PHP), the cyclotron frequency, the electron–phonon coupling strength and the transverse and the longitudinal effective confinement lengths are taken into account. The results show that the first excited state energy decreases (increases) when the temperature is increased at lower (higher) temperature region. And it is an increasing function of the chemical potential, the zero point of PHP, the cyclotron frequency and the electron–phonon coupling strength. Simultaneously, it is a decreasing one of the transverse and the longitudinal effective confinement lengths.