Modified Schrodinger Equation Research Articles

New bound state solutions of diatomic molecules and mass spectrum of heavy quarkonium with improved modified Kratzer potential plus screened Coulomb potential model in the framework of three-dimensional nonrelativistic noncommutative phase-space symmetries

Approximate analytical solutions of the modified Schrodinger equation have been obtained with a combination of two proposed potentials, called the improved modified Kratzer potential plus screened Coulomb (IMKSC) potential, using the approximation scheme to the centrifugal term for any l-states. We applied the generalized Bopp’s shift method and standard perturbation theory. IMKSC is a superposition of modified Kratzer potential plus screened Coulomb (MKSC) potential, and new terms appear as a result of the effects of the noncommutativity properties of space and phase potential on the MKSC potential. The new bound state energy eigenvalues for some diatomic molecules were obtained in terms of the discrete atomic quantum numbers (j,n,s,m), the infinitesimal NC phase-space parameters, the dissociation energy, the equilibrium internuclear separation, the depth of the potential, and the range of the potential. Furthermore, we have shown that the NC-Hamiltonian operator is the sum of the Hamiltonian operator of the MKSC potential, the perturbed spin-orbit, and the modified Zeeman operator. The new mass spectra of heavy quarkonium systems are calculated using the new energy spectrum expression. It appears as a combination of corresponding values in the literature plus an infinitesimal part that describes the deformation phase-space.

Nonrelativistic potential well problem in GUP formalism: Laplace transform approach

The Schrodinger equation is considered in the minimal length formalism with the potential well problem. The equation, in an approximate scheme, appears in fourth-order form, which has not been extensively discussed in the literature. We transform the problem into Laplace space and the wave functions as well as energy spectra of the modified Schrodinger equation are calculated using the basic properties of this integral transform. The bound and continuous states are discussed in full detail.

Femtosecond Beam Transformation Effects in Water, Enabling Increased Throughput Micromachining in Transparent Materials

Femtosecond lasers are widely applied in scientific and industrial fields. Recent trends in the laser market show decreasing prices for femtosecond units, which will ultimately lead to the opening of new markets that were inaccessible in the past due to the high costs of such systems. To this end, new techniques that enable micromachining of materials with increased efficiency are interesting. In this article, we demonstrate a technique that may be used for cutting and drilling various materials. By placing a layer of water on top of the samples and loosely focusing laser light on the surface, it was found that the micromachining throughput is increased by up to 10-fold as compared with micromachining without the water layer (conventional focusing in air), however, the main reasons for the increase in fabrication efficiency have not been fully understood until now. By modelling the propagation of the femtosecond pulses by means of the nonlinear modified Schrodinger equation through the water layer, we show that the increased throughput is attributed to the changing of the Gaussian intensity profile. In addition, we confirm these findings by numerically modelling the ablated crater formation.

Minimal length Schrödinger equation via factorisation approach

The fourth-order modified Schrodinger equation due to the generalised uncertainty principle is considered in one dimension with a box problem. The factorisation of fourth-order self-adjoint differential equations is then discussed and thereby the wave functions and energy spectra of the modified Schrodinger equation are derived.

On Higher-Order Wave Equations in GUP Formalism

In our short note, the fourth-order modified Schrodinger equation due to generalized uncertainty principle is considered in one dimension with box problem as a typical example. The problem is transformed to Laplace space and the analytical solutions are reported via basic properties the transform. The approach, unlike other techniques, has the potential to consider the modified wave equations in two and three dimensions using the complex analysis.

The Hamilton–Jacobi Analysis of Powers of Singular Lagrangians: A Connection Between the Modified Schrödinger and the Navier–Stokes Equations

Non-standard Lagrangians have gained recently an increasing interest in the theory of nonlinear differential equations, classical and quantum nonlinear dynamical systems. In this work, we discuss a number of dynamical systems characterized by powers of singular Lagrangians identified to non-standard Lagrangians based on the resulting Hamilton–Jacobi equation. A number of dynamical problems were addressed and a number of statements which support the non-standard Lagrangians formalism were postulated. After connecting the action to a certain complex wave function and in particular for the case of linear potentials, a link is established between the resulting modified Schrodinger equation which describes specific classes of quantum mechanical systems and the Navier–Stokes equation which describes the motion of viscous fluid matters.

New Exact Non-relativistic Energy Eigen Values for Modified Inversely Quadratic Hellmann Plus Inversely Quadratic Potential

In this current research, the solutions of modified Schrodinger equation (MSE) are presented for two companied potentials namely: modified inversely quadratic Hellmann potential and modified inversely quadratic potential (MIHQP), using generalization of Bopp’s shift method (instead to solving MSE with star product) and standard perturbation theory in extended quantum mechanics (EQM), we obtained modified Hamiltonian operator and corresponding modified eigenvalues in both three dimensional noncommutative space and phase (NC-3D: RSP) symmetries.

Cornell potential in generalized uncertainty principle formalism: the case of Schrödinger equation

The modified Schrodinger equation due to generalized uncertainty principle is considered with the Cornell potential. The problem is transformed into the momentum space and a quasi-exact analytical approach is used to report the solutions. The ground-state wave function as well as the set of equations determining the spectrum of the system are obtained and the special case of the vanishing minimal length parameter is recovered.

Cusp Interaction in Minimal Length Quantum Mechanics

The modified Schrodinger equation with a minimal length is considered under a Cusp potential which includes the exponential interaction. Next, exact analytical solutions of the problem are reported and thereby the scattering states as well as the corresponding transmission and reflection coefficients are reported.

Potential well and step potential within the framework of minimal length quantum mechanics

The potential well and the step potential are studied under the modified Schrodinger equation due to minimal length in an exact analytical manner. The scattering problems as well as the reflection and transmission parameters are reported.

Wavefunction delocalization in quantum dot arrays: an asymptotic analysis

Intermediate-band solar cells using quantum dot arrays (QDAs) are theoretically predicted to significantly increase the efficiency with which solar energy can be harvested. In the limit of identical quantum dots, the wavefunction for electrons in a QDA will be fully delocalized. Fully delocalized wavefunctions have been theoretically shown to reduce thermal losses and consequently increase photovoltaic device efficiency. However, even small nonuniformities can cause electrons to localize in a single quantum dot, negating any advantages from delocalized states. In this work a modified Schrodinger equation is used to model a two-dot array with nonuniform quantum dots and solved using perturbation methods. This result is extended to N-dot arrays, and several metrics are constructed to characterize the degree of delocalization. Our results, which compare favorably with numerical simulations, show explicitly how the amount of delocalization depends on key design parameters.

Modified Schrödinger Equation for Particles with Mass of the Order of Human Neuron Mass

In this paper the modified Schrodinger equation (MSE) for the particles with mass = mass of the human neuron is obtained and solved. Considering that neuron mass is of the order of Planck mass it was shown that for mass of the order of the human neuron mass the transition quantum → classical behavior can occurs. Moreover it was argued that the human brain can be described as the fluid of the Planck particles. It is interesting to observe that the Planck gas was created at the beginning of the Universe.

Supercontinuum generation in an anisotropic microstructure fiber with periodic modulation of hole ellipticity

The supercontinuum generation in an anisotropic microstructure fiber with periodic modulation of hole ellipticity has been numerically simulated. The structure proposed makes it possible to alternate fiber segments with positive and negative differences in group velocities, thus affecting the interaction of pulses with orthogonal polarizations. This configuration makes it possible to effectively control supercontinuum generation. The dynamics of polarized solitons in a microstructure fiber with high nonlinearity is simulated using the modified Schrodinger equation, including the stimulated Raman scattering and higher order dispersion.

Hamiltonian Systems Inspired by the Schrödinger Equation

Described is n-level quantum system realized in the n-dimensional Hilbert space H with the scalar product G taken as a dynamical variable. The most general Lag- rangian for the wave function and G is considered. Equations of motion and conservation laws are obtained. Special cases for the free evolution of the wave function with fixed G and the pure dynamics of G are calculated. The usual, first- and second-order modified Schrodinger equations are obtained.

Numerical analysis of four-wave mixing between picosecond mode-locked laser pulses in a tensile-strained bulk SOA

A numerical model of four-wave mixing between picosecond pulses in a tensile-strained bulk semiconductor optical amplifier is presented. The model utilizes a modified Schrodinger equation to model pulse propagation. The Schrodinger equation parameters such as the material gain first and second order dispersion, linewidth enhancement factors and optical loss coefficient were obtained using a previously developed steady-state model. The predicted four-wave mixing pulse characteristics show reasonably good agreement with experimental pulse characteristics obtained using Frequency Resolved Optical Gating. In particular simulations predict a large increase in the pulse pedestals of the FWM converted pulse, which is verified by experiment.

Governing equations of envelopes created by nearly bichromatic waves on deep water

In this paper, the author derives the modified Schrodinger equation that governs the envelope created by nearly bichromatic waves, which are defined by the waves whose energy is almost concentrated in two closely approached wavenumbers. The stability of the solution of the modified Schrodinger equation for nearly bichromatic waves on deep water is discussed and the fact that the Benjamin–Feir instability occurs in a condition is shown. Moreover, the solutions of the modified Schrodinger equation for nearly bichromatic waves on deep water are obtained and, in a special case, the solution becomes the standing wave solution is shown.

Modulation instability of electrohydrodynamic waves on liquid jet

An analytical study of slow modulation has been made of cylindrical interface between two inviscid streaming fluids, in the presence of a relaxation of electrical charges at the interface, and stressed by an axial electric field. A new technique based on the perturbation theory, to derive the non-linear evolution equations has been introduced. These equations are combined to yield a non-linear Ginzburg–Landau equation and a non-linear modified Schrödinger equation describing the evolution of wave packets. The linear analysis showed that the streaming has a destabilizing effect and the electric field has stabilizing influence associated with parameters condition involving the electric conductivity and permittivity of the fluids. While the non-linear approach indicated that the streaming may become unstable for sufficiently high velocities, with a new condition on the material properties, involving weak electric relaxation times in both fluids.

Numerical simulation of ballistic surface transport in cylindrical nanosystems

We study, by numerical simulations, the effect of topology on coherent electron transport through cylindrical junctions and bent cylindrical surfaces. The dynamics of a particle bound to a curved surface is described by a modified Schrodinger equation depending on two curvilinear coordinates. The modeling approach based on a finite-difference discretization of the latter equation is described, and a comparison with the standard solution of Schrodinger equation for flat surfaces is given. The effect of the geometrical parameters of the structures is reported.

Causal heat transport induced by zeptosecond laser pulses

The thermal phenomena induced by zeptosecond (10 m 21 s) laser pulses are discussed in this article. Considering the theoretical proposal of the lasetron , the Heaviside equation for heat transport on zeptosecond time scale is formulated. In the article, the modified Schrodinger equation (Janina Marciak-koz ^ owska and Miros ^ aw Koz ^ owski (2002). Lasers in Engineering , 12 , 53) for quantum phenomena on the zeptosecond time scale was also discussed.

Modified schrödinger equation for attosecond laser pulse interaction with matter

Recently the measurement of X-ray pulses approaching the attosecond frontier was published (M. Drescher et al ., Science 291 (2001) p. 1923). The attosecond laser pulse enables the study and control of the motion of electrons inside atoms. In this paper we develop and solve the modified Schrodinger equation (MSE) which describes the interaction of electrons with its surroundings in an atom. This interaction can be detected only using an attosecond laser pulse within the relaxation time of the interaction which is of the order of 10 attoseconds.