Pseudoharmonic Oscillator Research Articles

A Non-Relativistic 2D Quantum System and Its Thermo-Magnetic Properties with a Generalized Pseudo-Harmonic Oscillator

In this work, we examine the thermo-magnetic characteristics and energy spectra of a system exposed to both magnetic and Aharonov–Bohm (AB) fields with the existence of an interaction potential that is pseudo-harmonic. Explicit calculations of the eigen-solutions are performed with the expanded Nikiforov–Uvarov formalism. The confluent Heun function is used to represent the equivalent wave functions. If the AB and magnetic fields are gone, quasi-degeneracy in the system’s energy levels is shown by a numerical analysis of the energy spectrum. Additionally, we provided a visual representation of how the AB and magnetic fields affected the system’s thermo-magnetic characteristics. Our results show a strong dependence of thermo-magnetic properties on temperature, screening parameters, external magnetic fields, and AB fields.

Exact solutions of position-dependent mass Schrödinger equation with pseudoharmonic oscillator and its thermal properties using extended Nikiforov–Uvarov method

Exact solutions of position-dependent mass Schrödinger equation with pseudoharmonic oscillator and its thermal properties using extended Nikiforov–Uvarov method

On the pseudoharmonic oscillator as a model for the electronic potential-energy function of a diatomic molecule

On the pseudoharmonic oscillator as a model for the electronic potential-energy function of a diatomic molecule

Emission spectrum for a cascade-type three-level atom driven by optical field in photon added coherent state of PHO

A treatment of the interaction of a multi-photon cascade-type three-level atom in a cavity with a single-mode field initially in the photon added coherent states (PA-CSs) of pseudo-harmonic oscillator (PHO) is presented in this paper. The wavefunction corresponding to the system under consideration and the emission spectrum (ES) are obtained. It is shown that the properties of the ES are affected by the PA-CS of PHO parameters. The influence of the number of added photons to the CS of PHO on the dynamical behavior of the ES is investigated. The results showed that the behavior of the ES is strongly changed according to the CS of PHO parameters and its number of added photons. Symmetric peaks are generated around the vertical axis with increasing influence of some values of the initial field state parameters.

One-dimensional pseudoharmonic oscillator: classical remarks and quantum-information theory

Motion along semi-infinite straight line in a potential that is a combination of positive quadratic and inverse quadratic functions of the position is considered with the emphasis on the analysis of its quantum-information properties. Classical measure of symmetry of the potential is proposed and its dependence on the particle energy and the factor describing a relative strength of its constituents is described; in particular, it is shown that a variation of the parameter alters the shape from the half-harmonic oscillator (HHO) at to the perfectly symmetric one of the double frequency oscillator (DFO) in the limit of huge . Quantum consideration focuses on the analysis of information-theoretical measures, such as standard deviations, Shannon, Rényi and Tsallis entropies together with Fisher information, Onicescu energy and non–Gaussianity. For doing this, among others, a method of calculating momentum waveforms is proposed that results in their analytic expressions in form of the confluent hypergeometric functions. Increasing parameter modifies the measures in such a way that they gradually transform into those corresponding to the DFO what, in particular, means that the lowest orbital saturates Heisenberg, Shannon, Rényi and Tsallis uncertainty relations with the corresponding position and momentum non–Gaussianities turning to zero. A simple expression is derived of the orbital-independent lower threshold of the semi-infinite range of the dimensionless Rényi/Tsallis coefficient where momentum components of these one-parameter entropies exist which shows that it varies between 1/4 at HHO and zero when tends to infinity. Physical interpretation of obtained mathematical results is provided.

Exact solutions of kappa-dependent Schrödinger equation with quantum pseudo-harmonic oscillator and its applications for the thermodynamic properties in normal and superstatistics

The effects of the curvature parameters on the energy eigenvalues and thermodynamic properties of quantum pseudoharmonic oscillator are investigated within the framework of nonrelativistic quantum mechanics. By employing Nikiforov-Uvarov method, the energy spectra are obtained and used to study the ordinary statistics and q-deformed superstatistics as a function of temperature in the presence and absence of the curvature parameters. It is shown that the q-deformed supertatistics properties of the quantum pseudoharmonic oscillator reduce to the ordinary statistical properties in the absence of the deformation parameter. Finally, our results are illustrated graphically to show the behaviour of the energy spectra and thermodynamic properties for the three curvature parameters:kappa = - 1,,,kappa = 1,,{text{and}},,kappa = 0.

Retracted: Exact solutions of the Schrödinger equation using extended Nikiforov-Uvarov formalism for generalized pseudo-harmonic oscillator

The Schrodinger equation with generalized pseudo-harmonic oscillator (GPHO) is transformed into a form that is compatible with extended Nikiforov-Uvarov (ENU) formalism, and its exact solutions are obtained in three and N-dimensions using this formalism. The energy spectrum for the GPHO was obtained in closed form, and the wave function was determined using the biconfluent Heun differential equation. Special cases are deduced, and some numerical results are shown to illustrate the behaviour of the bound state energies at different quantum states for various values of potential parameter; lambda. In addition, the thermodynamic property expressions for GPHO are obtained in closed form, and their variation with temperature-dependent parameters is discussed extensively for various values of lambda. Our results agree with those obtained in the literatures.

The bound-state solutions of the one-dimensional pseudoharmonic oscillator

We study the bound states of a quantum mechanical system consisting of a simple harmonic oscillator with an inverse square interaction, whose interaction strength is governed by a constant $\alpha$. The singular form of this potential has doubly-degenerate bound states for $-1/4\leq\alpha<0$ and $\alpha>0$; since the potential is symmetric, these consist of even and odd-parity states. In addition we consider a regularized form of this potential with a constant cutoff near the origin. For this regularized potential, there are also even and odd-parity eigenfunctions for $\alpha\geq-1/4$. For attractive potentials within the range $-1/4\leq\alpha<0$, there is an even-parity ground state with increasingly negative energy and a probability density that approaches a Dirac delta function as the cutoff parameter becomes zero. These properties are analogous to a similar ground state present in the regularized one-dimensional hydrogen atom. We solve this problem both analytically and numerically, and show how the regularized excited states approach their unregularized counterparts.

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.

Path integral analysis from the D-dimensional generalized displacement operator, and some of their applications

Recently, H. Benzair et al. [Mod. Phys. Lett. A 35, 2050246 (2020).] formulated in one dimension the nonrelativistic propagator for position-dependent mass (PDM) from the generalized displacement operator approach. According to the path integral formulation, we generalize this process in [Formula: see text]-dimensional space. As a result, the wave functions are obtained analytically for the pseudo-harmonic oscillator and the inverse square plus Coulomb potentials, and the corresponding energy spectrum are studied. In addition, the effects of PDM on the canonical partition function and other thermodynamic functions have been extracted. The limit cases are then deduced for a small parameter.

A new generalization of nonlinear coherent states for the pseudoharmonic oscillator

We construct two-parameters family of nonlinear coherent states by replacing the factorial in coefficients $$z^n/\sqrt{n!}$$ of the canonical coherent states by a specific generalized factorial $$x_n^{\gamma ,\sigma }!$$ where parameters $$\gamma $$ and $$\sigma $$ satisfy some conditions for which the normalization condition and the resolution of identity are verified. The obtained family is a generalization of the Barut–Girardello coherent states and those of the philophase states. In the particular case of parameters $$\gamma $$ and $$\sigma $$ , we attache these states to the pseudoharmonic oscillator depending on two parameters $$\alpha ,\beta > 0$$ . The obtained nonlinear coherent states are superposition of eigenstates of this oscillator. The associated Bargmann-type transform is defined and we derive some results.

Generalized quantum similarity index: An application to pseudoharmonic oscillator with isospectral potentials in 3D

AbstractExact solutions of a pseudoharmonic oscillator and a family of isospectral potentials are investigated in spherical coordinates. The entropic moment, generalized quantum similarity index, and some quantum information measures are investigated analytically and numerically for two density functions of two quantum systems with same energy and one quantum system with different energies. Analytical results are compared for 19 selected molecules and verified by some physical and artificial values of the spectroscopic parameters.

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.

Quantum phase and nonclassical properties of a two qubits interacting with a radiation field in PACS-PHO

The problem of interaction falls between a two qubits and a radiation field based on PACS-PHO (Photon Added Coherent States of Pseudo-Harmonic Oscillator) without and with time-varying frequency of the field is considered in this paper. The solution with the analytic method for the wave function of the whole system is applied to describe different quantum measuring. We examine the entanglement between the quantum subsystems of the whole system by considering the qubits concurrence and qubit-field von Neumann entropy. We show the time evolution of the statistical properties of the PACS-PHO during their interaction with the two qubits. Finally, under the main physical parameters we reveal how the geometric phase of the system state can be affected and changed. Hence, according quantum mechanics this studying can open a new perspective for the experimental observation of macro realism.

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.

Emission Spectrum and Nonclassical Properties of an Atom–Field System Under an Intensity-Dependent Field

In this paper, we investigate the emission spectrum of a two-level atomic system interacting with an optical radiation field based on photon-added coherent states of a pseudo-harmonic oscillator (PACSPHO). Also, the purity of the optical field initially prepared in the PACS-PHO is studied through the evolution of the field entropy. We examine the influence of the intensity-dependent field and the photon-transition number on the dynamic behavior of the emission spectrum and field purity. We explore the link between the field purity and the emission spectrum during the time evolution. Finally, we show how the emission spectrum is affected and changed according to the main physical parameters. We find that there is some kind of correlation between the emission spectrum and the field purity, which will be useful in different applications of quantum physics and spectroscopy.

Applications of the extended uncertainty principle in AdS and dS spaces

All commutation relations are modified in (anti)-de Sitter background and the Heisenberg uncertainty principle is changed to the so-called extended uncertainty principle (EUP). In this scenario, the commutators between position and momentum operators are functions of the position space variables, instead of a constant and the coordinate representation of the momentum operators for this model becomes coordinate dependent. In the AdS space, a lower bound on momentum uncertainty arises, which is not present in the dS space. In this paper, we present an exact solution of the D -dimensional free particle, the harmonic oscillator and pseudoharmonic oscillator in AdS and dS spaces. The eigenfunctions are determined for both cases and the energy eigenvalues are obtained.

Photon added coherent states of the parity deformed oscillator

Using the parity deformed Heisenberg algebra (RDHA), we first establish associated coherent states (RDCSs) for a pseudo-harmonic oscillator (PHO) system that are defined as eigenstates of a deformed annihilation operator. Such states can be expressed as superposition of an even and odd Wigner cat states.[Formula: see text] The RDCSs minimize a corresponding uncertainty relation, and resolve an identity condition through a positive definite measure which is explicitly derived. We introduce a class of single-mode excited coherent states (PARDCS) of the PHO through “m” times application of deformed creation operators to RDCS. For the states thus constructed, we analyze their statistical properties such as squeezing and sub-Poissonian statistics as well as their uncertainty relations.

Quantum Quantifiers for an Atom System Interacting with a Quantum Field Based on Pseudoharmonic Oscillator States.

We develop a useful model considering an atom-field system interaction in the framework of pseudoharmonic oscillators. We examine qualitatively the different physical quantities for a two-level atom (TLA) system interacting with a quantized coherent field in the context of photon-added coherent states of pseudoharmonic oscillators. Using these coherent states, we solve the model that exhibits the interaction between the TLA and field associated with these kinds of potentials. We analyze the temporal evolution of the entanglement, statistical properties, geometric phase and squeezing entropies. Finally, we show the relationship between the physical quantities and their dynamics in terms of the physical parameters.

Quantum pseudodots under the influence of external vector and scalar fields

We study the spherical quantum pseudodots in the Schrödinger equation by using the pseudo-harmonic plus harmonic oscillator potentials considering the effect of the external electric and magnetic fields. The finite energy levels and the wave functions are calculated. Furthermore, the behavior of the essential thermodynamic quantities such as, the free energy, the mean energy, the entropy, the specific heat, the magnetization, the magnetic susceptibility, and the persistent currents are also studied by using the characteristic function. Our analytical results are found to be in good agreement with the other works. The numerical results on the energy levels as well as the thermodynamic quantities have also been given.