Schrodinger Equation Research Articles

The possible KK¯* and DD¯* bound and resonance states by solving the Schrodinger equation

The Schrodinger equation with a Yukawa type of potential is solved analytically. When different boundary conditions are taken into account, a series of solutions are indicated as a Bessel function, the first kind of Hankel function and the second kind of Hankel function, respectively. Subsequently, the scattering processes of KK¯* and DD¯* are investigated. In the KK¯* sector, the f 1(1285) particle is treated as a KK¯* bound state, therefore, the coupling constant in the KK¯* Yukawa potential can be fixed according to the binding energy of the f 1(1285) particle. Consequently, a KK¯* resonance state is generated by solving the Schrodinger equation with the outgoing wave condition, which lies at 1417 − i18 MeV on the complex energy plane. It is reasonable to assume that the KK¯* resonance state at 1417 − i18 MeV might correspond to the f 1(1420) particle in the review of the Particle Data Group. In the DD¯* sector, since the X(3872) particle is almost located at the DD¯* threshold, its binding energy is approximately equal to zero. Therefore, the coupling constant in the DD¯* Yukawa potential is determined, which is related to the first zero point of the zero-order Bessel function. Similarly to the KK¯* case, four resonance states are produced as solutions of the Schrodinger equation with the outgoing wave condition. It is assumed that the resonance states at 3885 − i1 MeV, 4029 − i108 MeV, 4328 − i191 MeV and 4772 − i267 MeV might be associated with the Zc(3900), the X(3940), the χ c1(4274) and χ c1(4685) particles, respectively. It is noted that all solutions are isospin degenerate.

Approximate solutions for diatomic molecules under combined potentials in a global monopole and Aharonov–Bohm flux field

AbstractBound state energy eigensolutions of nine different diatomic molecules, specifically, , TiH, , CO, NO, ScH, CrH, HCl and LiH, placed in a point‐like global monopole, have been calculated by solving the time‐independent Schrödinger equation (SE). The molecules are confined by the Aharonov–Bohm (AB) flux field and the interaction potential among the charged particles is governed by the combined screened modified Kratzer potential (SMKP) plus Hulthén potential model. Three other special cases of the interaction potential have also been discussed here. Asymptotic iteration method has been used for the mathematical calculations. It is difficult to solve the SE exactly for any non‐zero values of the azimuthal quantum number due to the presence of the centrifugal barrier term. The well‐known Pekeris approximation technique for the terms and has taken into consideration for the purpose of performing numerical computations connected to an arbitrary state. The outcomes of this study are in reasonable agreement with the results of previous research on SMKP, Kratzer‐Fues potential, and modified Kratzer potential in the Minkowski space. It is observed that the energy spectra of the diatomic molecules suffer considerable change due to the effects of the background AB‐flux field and topological defect parameter.

Electric field-induced modulation of electronic and optical properties in doped CdTe/CdS core/shell quantum dots embedded in an oxide matrix

This work presents a theoretical analysis of a CdTe/CdS core/shell quantum dots embedded in a dielectric oxide matrix under the influence of hydrogenic impurity and the applied electric field intensity. The eigenstates and their corresponding eigenfunctions are computed by solving the Schrodinger equation using the finite element method within the effective mass approximation. The first-order linear and third-order nonlinear optical absorption coefficients as well as the refractive index changes are computed based on the compact density matrix approach. The obtained result shows that the first-order linear and third-order nonlinear optical properties are more pronounced with the electric field, surrounding oxide matrix and the donor impurity effects. However, the first-order linear and third-order nonlinear optical absorption coefficients and refractive index changes can experience a red or blue shift under the influence of electric field, oxide matrix and hydrogenic impurity. In addition, under all conditions, the height peaks of these optical properties can be raised (fall). Our findings demonstrate the critical importance of considering the roles of electric field, the presence of donor impurity, and the capped dielectric oxide matrix in the design and fabrication of core–shell-based optoelectronic devices.

Bifurcation study, phase portraits and optical solitons of dual-mode resonant nonlinear Schrodinger dynamical equation with Kerr law non-linearity

This study investigates the dynamic characteristics of the dual-mode resonant non-linear Schrodinger equation with a Bhom potential. Hydrodynamics, nonlinear optical fibre communication, elastic media, and plasma physics are just a few of the mathematical physics and engineering applications for this model. The study aims to achieve two main objectives: first, to discuss bifurcation analysis, and second, to extract optical soliton solutions using the extended hyperbolic function method. The study successfully derives various wave solutions, including bright, singular, periodic singular and dark solitons, based on the governing model. The findings conferred in this article show a crucial advancement in understanding the propagation of waves in non-linear media. Additionally, bifurcation of phase portraits of ordinary differential equation consistent with the partial differential equation under consideration is conducted. We also highlight specific constraint conditions that ensure the presence of these obtained solutions. The existing literature shows that these methods are first time applied on this model.

Non-Kerr Law Medium: Optical Solitons and their Perturbation

This investigation focuses on the perturbation analysis of optical solitons within a medium in accordance with the non-Kerr law. In the field of partial differential equations, generalized nonlinear Schrodinger equation (GNLSE) is an integrable nonlinear equation. In the non-Kerr law non-linear medium, GNLSE is utilized for doing an analytical analysis of soliton perturbations as well as the soliton itself. In case of non-Kerr law instance, the application of quasi-stationarity results in a soliton that is very close to being approximated. Several edge scenarios of nonlinearity that vary from the Kerr law remain the primary focus of the current study. Although it was found that a disturbance of the nonlinear damping kind remains present, equations can be solved to find solutions. Consequently, GNLSE cannot be integrated because of the presence of higher-order dispersion.

On the Oscillation of a Class of Conformable Schrodinger Equations

In this article, we have derived a new oscillation criteria for a class of conformable Schrodinger equations. Based on the generalized Riccati technique, the results were obtained here. Also we have extended the Hartman-Winter oscillation criteria to conformable Schrodinger equation.

Application of the G’/G Expansion Method for Solving New Form of Nonlinear Schrödinger Equation in Bi-Isotropic Fiber

Bi-isotropic media (chiral and non-reciprocal) present an outstanding challenge for the scientific community. Their characteristics have facilitated the emergence of new and remarkable applications. In this paper, we focus on the novel effect of chirality, characterized through a newly proposed formalism, to highlight the nonlinear effect induced by the magnetization vector under the influence of a strong electric field. This research work is concerned with a new formulation of constitutive relations. We delve into the analysis and discussion of the family of solutions of the nonlinear Schrödinger equation, describing the pulse propagation in nonlinear bi-isotropic media, with a novel approach to constitutive equations. We apply the extended -expansion method with varying dispersion and nonlinearity to define certain families of solutions of the nonlinear Schrödinger equation in bi-isotropic (chiral and non-reciprocal) optical fibers. This clarification aids in understanding the propagation of light with two modes of propagation: a right circular polarized wave (RCP) and a left circular polarized wave (LCP), each having two different wave vectors in nonlinear bi-isotropic media. Various novel exact solutions of bi-isotropic optical solitons are reported in this study. Introduction: The investigation of exact solutions for nonlinear partial differential equations (PDEs) holds significant importance in understanding nonlinear physical phenomena. Nonlinear waves manifest across various scientific domains, notably in optical fibers and solid-state physics. In recent years, several potent methodologies have emerged for identifying solitons and periodic wave solutions of nonlinear PDEs. These include the -expansion method [1-6], the new mapping method [9-10], the method of generalized projective Riccati equations [11-16], and the expansion method [17]. Consequently, an original mathematical approach is proposed to evaluate nonlinear effects in bi-isotropic optical fibers, stemming from magnetization under the influence of a strong electric field [19-20]. The extended -expansion method emerges as a potent technique for deriving solution families of the nonlinear Schrödinger equation in bi-isotropic optical fibers. This method employs a perturbation expansion in powers of the dimensionless parameter and is applicable for both weak and strong nonlinearities. It accommodates varying dispersion and nonlinearity, rendering it suitable for modeling a wide array of optical fibers. Results and Conclusion: This investigate is concerned with a new formulation of constitutive relation linking to the magnetic effect, to understand rigorously the physical nature of biisotropic effects and to generalize the main macroscopic models. We inferred the nonlinear Schrodinger equation for a bi-isotropic medium term with a nonlinear term of magnetizing. In this article, the extended -expansion method is a powerful technique for determining a family of solutions of the nonlinear Schrödinger equation in bi-isotropic optical fibers. This method is based on the use of a perturbation expansion in powers of the dimensionless parameter, and it is valid for both weak and strong nonlinearities. The method allows for the inclusion of varying dispersion and nonlinearity, making it well-suited for modeling a wide range of optical fibres. Overall, the extended -expansion method is a valuable tool for understanding the dynamics of nonlinear optical systems, and it is expected to have a wide range of applications in the field of nonlinear optics.

Laser beam effect on the entanglement of elastic collisions in quantum plasma

In the quantized field formalism, using Kramers–Henneberger unitary transformation as the semi-classical counterpart of Block–Nordsieck transformation, the dynamics of entanglement during the low energy scattering processes in bi-partite systems at the presence of a laser beam fields are studied. The stationary-state Schrodinger equation for the quantum scattering process is obtained for such systems. Then, using partial wave analysis, we introduce a new form of entanglement fidelity considering the effect of high-intensity laser beam fields. The effective potential of hot quantum plasma including plasmon and quantum screening effects is used to obtain the entanglement fidelity ratio as a function of the laser amplitude, and plasmon and Debye length parameters for the elastic electron-ion collisions. It is shown that the plasma free electrons oscillations under interaction with laser beam fields improve the correlations between charged particles and consequently lead to the increase in the system entanglement.

Impact of combined electric and magnetic fields on the physical properties of GaAs variant quantum ring quarter cross-section in presence of an off-center shallow donor impurity

In this study, we explored the complex effects of electric fields in three unique directions and axial magnetic field on a GaAs-Variant Quantum Ring Quarter Cross-Section (VQRQCS), particularly when there is an off-center shallow donor impurity. The investigation explores the impact of these fields on various physical attributes, including electronic energy, binding energy, magnetic shift, Stark shift, average electron impurity distance, and diamagnetic susceptibility. Using effective mass approximation and three-dimensional finite difference methods we solved the Schrodinger equation. Our result shows that the geometric radius of the VQRQCS has an essential impact on electronic energy. Notably, as the radius increases, the electronic energy decreases, regardless of the presence of fields. In particular, we found that magnetic fields amplify the electronic energy of the ground state. The angle of curvature of the nanostructure and the direction of the electric field also play an important role. Additionally, the electron–impurity binding energy decreases with the growth of the nanostructure, with external fields intensifying this effect. The average distance between the electron and the impurity, analyzed in the context of simultaneously applied fields, provides insight into the Coulomb interaction. Diamagnetic susceptibility, measuring the response of a material to an external magnetic field, is studied, indicating opposition to the external field. In summary, this research highlights the nuanced interactions between electric and magnetic fields that determine the properties of a GaAs quantum ring, providing critical insights for quantum ring-based technological advancements.

Binding Energies and Optical Properties of Power-Exponential and Modified Gaussian Quantum Dots.

We examine the optical and electronic properties of a GaAs spherical quantum dot with a hydrogenic impurity in its center. We study two different confining potentials: (1) a modified Gaussian potential and (2) a power-exponential potential. Using the finite difference method, we solve the radial Schrodinger equation for the 1s and 1p energy levels and their probability densities and subsequently compute the optical absorption coefficient (OAC) for each confining potential using Fermi's golden rule. We discuss the role of different physical quantities influencing the behavior of the OAC, such as the structural parameters of each potential, the dipole matrix elements, and their energy separation. Our results show that modification of the structural physical parameters of each potential can enable new optoelectronic devices that can leverage inter-sub-band optical transitions.

The Application of Spectroscopic Parameters for Computing the Energy Spectrum of Selected Diatomic Molecules (VH, LiH, TiC and CuLi)

A basic theoretical model known as the Schrodinger equation is utilized to explain the physics of the waveform, a phenomenon in quantum mechanics. The whole characterization of a technique’s components is included within the wave function. There are several aspects of the Schrodinger equation’s numerical solution. In this work, we determined mathematically the eigenvalues and characteristic functions of the Eckart-Hellmann potential. This study adopted an estimating strategy for solving the problem recommended by the Nikiforov–Uvarov approach and employed the Greene–Aldrich approximation. The aim was determining bound energies and applying the findings to particular diatomic molecules and their spectroscopic parameters. By contrasting our eigenvalue data with extra numerical data collected by other scholars, the good outcomes of our technique were validated.

Simulation Analysis of Factors Affecting the Quantum Tunneling Effect in 1D Double Potential Barriers Structures

The working principle of a large number of modern scientific equipment has been applied to the quantum tunneling effect. Although the explanations for the relevant principles of this effect are clarified, the calculation process is very complex and difficult to understand. Previous studies combine specific applications without theoretical model references. This study adopts the method of using the time-independent Schrodinger equation to solve the wave function, which is more convenient to obtain the expression of transmission probability. Then, one discusses the relationship between transmission probability and potential barrier width, potential barrier spacing, and incident particle energy. The experimental results show that the transmission probability decreases exponentially from 1 to 0 as the potential barrier width gradually increases. As the potential barrier width increases, the transmission probability exhibits a clear periodic oscillation relationship, the oscillation period remains unchanged, and this paper derives the relationship between the oscillation period and the potential barrier width. As the incident energy of particles gradually increases, the transmission probability exhibits periodic changes, and the minimum value of transmission probability increases with the periodic changes. Based on the analysis, the smaller the potential barrier width, the greater the incident energy, and the more likely quantum tunneling occurs.

Analysis of Electron Double Barrier Tunneling Based on Python

Tunneling is a common phenomenon in microphysics, and resonant tunneling is a tunneling phenomenon under special conditions. Double barrier tunneling is an important quantum mechanical phenomenon, which has important application and research value in condensed matter physics, semiconductor devices, quantum mechanics, and nanotechnology. This study takes the double barrier as an example to observe electron tunneling and find out the influence of different parameters on the tunneling effect. In this study, the wave function is calculated by using the method of Schrodinger equation and transpose matrix, and the image is drawn by Python and numerical operation. In this study, it is found that the barrier width is inversely proportional to the transmittance, and the transmittance and reflectance will change periodically with the distance between the two barriers, and the electrons will reach full transmission at a certain incident energy value. Studying the characteristics and mechanisms of double barrier tunneling helps develop new quantum technologies and devices and promotes technological innovation in related fields.

A hybrid variational method for beam propagation and interaction in a graded-index nonlinear waveguide

The hybrid variational method can be used to simplify multidimensional numerical simulations. We examine the applicability of this method to study the nonlinear propagation of a single beam and the interference of two spatial soliton beams in a graded-index optical waveguide governed by a two-dimensional nonlinear Schrodinger equation. We classified three distinct regimes of the dynamics that emerge during single Gaussian beam propagation, corresponding to beam decay, breather formation, and self-focusing. When two spatial soliton beams were set up to interfere in the waveguide, we identified the boundary where the nonlinear interaction during the interference led to excitation or self-focusing. These quite involved dynamics were used to test the predictive power of our variational models by comparing them with direct numerical simulations, obtaining good agreement.

A Modified Crank-Nicolson Method for Numerical Solution of the Linear Time-Dependent Schrodinger Equation

This paper presents the effectiveness of the solution of the time-dependent Schrodinger equation using the modified Crank-Nicolson Method (MCNM). The method was developed through finite difference approximation. To demonstrate the effectiveness of this approach, three different problems were tested with these approaches by using MATLAB soft code. Also, this research verifies that, in the presence or absence of potential energy, the modified Crank-Nicolson method for solving the time-dependent Schrödinger equation is accurate, convergent, and computationally efficient.

Entire Sign-Changing Solutions to the Fractional Critical Schrodinger Equation

Entire Sign-Changing Solutions to the Fractional Critical Schrodinger Equation

Legendre Polynomials are Associated in the Schrodinger Polar Equation of Helium Ions

The helium ion is one of the ions classified as a hydrogenic atom because it has only one electron in its outer orbital so that the helium ion problem can be solved using the Schrodinger equation approach. The Schrodinger equation of the polar part of the helium ion can be solved by the associated legendary polynomial function, . The polar function expresses the angle formed by the vector of the electron's position relative to the z-axis of the helium ion's nuclear position. And it is produced that the polar function of the hydrogenic atom has the same polar function both in position space and in momentum space .

Electronic transport properties in GaAs/AlGaAs finite superlattice of cylindrical quantum wires

In this paper, we have studied a theoretical and numerical investigation of the electronic properties of finite cylindrical quantum wires (CQWRs), constituted by the periodic alteration of two semiconductor materials of CQWRs GaAs/AlGaAs in the axial direction, the structure sandwiched between two substrates GaAs. The electronic band structure and the electronic transmission spectrum are obtained by means of Green’s function approach, taking into account the impact of connection barriers. Our results reveal that the electronic energy levels of CQWRs consist of alternating passbands and bandgaps. The coincidence of incoming electronic waves with these discrete electronic energy levels leads to electron transport during the CQWRs superlattice. We employed an effective mass model dependent on the cell position in the axial direction to solve the Schrodinger equation. This model was adjusted to reflect variations in the confining potentials while accounting for changes in the radial direction. When the radius of the structure is relatively small the electronic states tend towards higher energies due to geometrical confinement. On the other hand, as the radius increases, the passbands and bandgaps move to lower energies. Similarly, the pseudogaps turn into full gaps, and their width increases, and this feature is also observed when the number of cells increases. This property is due to the interaction between the neighboring electrons and the eigenstates of the CQWRs. In addition, the passbands and band gaps shift to high energy when the barrier concentration increases, and the width of band gaps increases also. Finally, we have demonstrated the theoretical design of an optoelectronic device for filtering electronic waves by geometrical and physical parameters, whose electronic band structure of this finite CQWRs superlattice can be controlled.

Ion temperature gradient mode modulational stability analysis with cairn’s distribution

In this manuscript, we have studied electron-ion plasma with inhomogeneity in equilibrium number density and temperature. Ions are the dynamic species, and lighter particles in plasma obey the cairn’s distribution. We introduce Brajinskii’s equation for dynamic species and get the linear dispersion relation and the nonlinear Schrodinger equation by the reduction perturbation method. From the linear dispersion relation, we found the mode frequency and phase velocity, while from the nonlinear Schrodinger equation, we obtained the stability and instability of the ion temperature gradient mode modulation. Findings show that phase velocity is dependent on the superthermality coefficient and other plasma parameters like ion temperature, ion density, and mode parameter η i . Further, the modulational stability and instability of the mode vary with the superthermality coefficient and other plasma parameters, especially the η i . We can apply these observations equally to the laboratory as well as to the space plasma.

Pulse interaction induced systematic errors in dual comb spectroscopy

Systematic errors are observed in dual comb spectroscopy when pulses from the two sources travel in a common fiber before interrogating the sample of interest. When sounding a molecular gas, these errors distort both the line shapes and retrieved concentrations. Simulations of dual comb interferograms based on a generalized nonlinear Schrodinger equation highlight two processes for these systematic errors. Self-phase modulation changes the spectral content of the field interrogating the molecular response but affects the recorded spectral baseline and absorption features differently, leading to line intensity errors. Cross-phase modulation modifies the relative inter-pulse delay, thus introducing interferogram sampling errors and creating a characteristic asymmetric distortion on spectral lines. Simulations capture the shape and amplitude of experimental errors which are around 0.1% on spectral transmittance residuals for 10 mW of total average power in 10 meters of common fiber, scaling up to above 0.6% for 20 mW and 60 m.