Related papers: Linear Potentials, Airy Wave Packets and Airy Tran…

In this paper we numerically solve the time dependent Schr\"odinger equation for scenarios using wave packets. These examples include the free wave packet, which we use to show the difference between group and phase velocities, the packet…

Analytical solutions to the time-dependent Shr\"{o}dinger equation in one dimension are developed for time-independent potentials, one consisting of an infinite wall and a repulsive delta function. An exact solution is obtained by means of…

We study the massless limit of the Klein-Gordon (K-G) equation in 1+1 dimensions with static complex potentials as an attempt to give an alternative, but equivalent, representation of plane electromagnetic (em) wave propagation in active…

In this paper, we determine the wave front set of solutions to the Schr\"{o}dinger equation with time-dependent magnetic fields. We considered time-dependent and `not so small' magnetic fields through the method using the wave packet…

We prove that the effective low-energy, nonlinear Schroedinger equation for a particle in the presence of a quasiperiodic potential is the potential-free, nonlinear Schroedinger equation on noncommutative space. Thus quasiperiodicity of the…

This paper considers the question of global in time existence and asymptotic behavior of small-data solutions of nonlinear dispersive equations with a real potential $V$. The main concern is treating nonlinearities whose degree is low…

A set of factorization energies is introduced, giving rise to a generalization of the Schr\"{o}dinger (or Infeld and Hull) factorization for the radial hydrogen-like Hamiltonian. An algebraic intertwining technique involving such…

In this study, we examine the asymptotic behavior of solutions to nonlinear Schr\"{o}dinger equations with time-dependent harmonic oscillators and prove the time-decay property of solutions in the case of a long range power type…

We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support a tridiagonal matrix representation of the wave operator. Doing so results in exactly solvable problems with a…

By using the recent mathematical tools developed in quaternionic differential operator theory, we solve the Schroedinger equation in presence of a quaternionic step potential. The analytic solution for the stationary states allows to…

It is common practice to approximate a weakly nonlinear wave equation through a kinetic transport equation, thus raising the issue of controlling the validity of the kinetic limit for a suitable choice of the random initial data. While for…

Here we present a transformation that maps the Schrodinger equation of quantum mechanics to the incompressible Euler equations of fluid mechanics. The transformation provides a wave solution and a potential function based on fluid…

We review recent progress in the dynamics of nonlinear lattice waves in heterogeneous media, which enforce complete wave localization in the linear wave equation limit, especially Anderson localization for random potentials, and Aubry-Andre…

We consider a time-dependent one-dimensional nonlinear Schroedinger equation with a symmetric potential double well represented by two delta interactions. Among our results we give an explicit formula for the integral kernel of the unitary…

This paper establishes new estimates for linear Schroedinger equations in R^3 with time-dependent potentials. Some of the results are new even in the time-independent case and all are shown to hold for potentials in scaling-critical,…

We consider the long time dynamics of nonlinear Schr\"odinger equations with an external potential. More precisely, we look at Hartree type equations in three or higher dimensions with small initial data. We prove an optimal decay estimate,…

Due to the space and time dependence of the wave function in the time dependent Schroedinger equation, different boundary conditions are possible. The equation is usually solved as an ``initial value problem'', by fixing the value of the…

We provide simple examples of closed-form Gaussian wavepacket solutions of the free-particle Schrodinger equation in one dimension which exhibit the most general form of the time-dependent spread in position, namely (Delta x_t)^2 = (Delta…

This work deals with Schr\"odinger equations with quadratic and sub-quadratic Hamiltonians perturbed by a potential. In particular we shall focus on bounded, but not necessarily smooth perturbations. We shall give a representation of such…

Hagedorn functions are carefully constructed generalizations of Hermite functions to the setting of many-dimensional squeezed and coupled harmonic systems. Wavepackets formed by superpositions of Hagedorn functions have been successfully…