Related papers: Fractional Schr\"odinger equation and time depende…
How to accurately solve time-dependent Schr\"odinger equation is an interesting and important problem. Here, we propose a novel method to obtain the exact Floquet solutions of the Schr\"odinger equation for periodically driven systems by…
We study the uncoupled space-time fractional operators involving time-dependent coefficients and formulate the corresponding inverse problems. Our goal is to determine the variable coefficients from the exterior partial measurements of the…
In this work, we construct time-dependent potentials for the Schr\"odinger equation via supersymmetric quantum mechanics. The generated potentials have a quantum state with the property that after a particular threshold time $t_F$, when the…
In this manuscript we investigate the existence and uniqueness of an impulsive fractional dynamic equation on time scales involving non-local initial condition with help of Caputo nabla derivative. The existency is based on the Scheafer's…
The dielectric susceptibility of most materials follows a fractional power-law frequency dependence that is called the "universal" response. We prove that in the time domain this dependence gives differential equations with derivatives and…
The Caputo time-derivative is usually defined pointwise for well-behaved functions, say, for continuously differentiable functions. Accordingly, in the theory of the partial fractional differential equations with the Caputo derivatives, the…
A global solution of the Schr\"odinger equation for explicitly time-dependent Hamiltonians is derived by integrating the non-linear differential equation associated with the time-dependent wave operator. A fast iterative solution method is…
In this work we investigate an inverse problem of recovering a time-dependent potential in a semilinear subdiffusion model from an integral measurement of the solution over the domain. The model involves the Djrbashian--Caputo fractional…
We present new approaches for solving constrained multicomponent nonlinear Schr\"odinger equations in arbitrary dimensions. The idea is to introduce an artificial time and solve an extended damped second order dynamic system whose…
We reexamine the general solution of a Schr\"{o}dinger equation in the presence of a time-dependent linear potential in configuration space based on the Lewis-Riesenfeld framework. For comparison, we also solve the problem in momentum space…
In the paper, the initial-boundary value problems to a semilinear integro-differential equation with multi-term fractional Caputo derivatives are analyzed. A particular case of this equation models oxygen diffusion through capillaries.…
Diffraction in time of a particle confined in a box which its walls are removed suddenly at $t=0$ is studied. The solution of the time-dependent Schr\"{o}dinger equation is discussed analytically and numerically for various initial…
We propose a method for solving the time independent Schr\"odinger equation based on the von Neumann (vN) lattice of phase space Gaussians. By incorporating periodic boundary conditions into the vN lattice [F. Dimler et al., New J. Phys.…
The derivation of the time dependent Schr\"odinger equation with transversal and longitudinal relaxation, as the quantum mechanical analog of the classical Landau-Lifshitz-Bloch equation, has been described. Starting from the classical…
The simplest nonlinear Schrodinger equation that contains the time derivative of the probability density is investigated. This equation has the same stationary solutions as its linear counterpart, and these solutions are the eigenstates of…
In this paper we study the effect of the subordination by a general random time-change to the solution of a model on spatial ecology in terms of its evolution density. In particular on traveling waves for a non-local spatial logistic…
We present an elementary approach to observe frequency cascade on forced nonlinear Schr{\"o}dinger equations. The forcing term (which may also appear as a potential term instead) consists of a constant term, perturbed by a modulated…
In a fractional Cauchy problem, the usual first order time derivative is replaced by a fractional derivative. This problem was first considered by \citet{nigmatullin}, and \citet{zaslavsky} in $\mathbb R^d$ for modeling some physical…
We consider d-dimensional time dependent Schr\"odinger equations on the Hilbert space of square integrable functions. We assume magnetic and scalar potentials are almost critically singular with respect to spatial variables both locally and…
We present a new parallel numerical method for solving the non-stationary Schr\"odinger equation with linear nonlocal condition and time-dependent potential which does not commute with the stationary part of the Hamiltonian. The given…