A novel numerical approach to solving Schr odinger's equation as applied to quantum well heterostructures is described. The quantum mechanical energy subbands, wave functions and charge density are calculated based on a two-directional fourthorder Runge-Kutta (RK4) algorithm. The algorithm is applied to well-de ned quantum well structures. Results are compared with analytic solutions to ensure...

We consider the linear stability and structural stability of non-ground state traveling waves of a pair of coupled nonlinear Schrr odinger equations (CNLS) which describe the evolution of co-propagating polarized pulses in the presence of birefringence. Viewing the CNLS equation as a Hamiltonian perturbation of the Manakov equations, we nd parameter regimes in which there are two stable familie...

A family of predictor-corrector exponential Numerov-type methods is developed for the numerical integration of the one-dimensional Schrr odinger equation. The formula considered contains certain free parameters which allow it to be tted automatically to exponential functions. The new methods are very simple and integrate more exponential functions than both the well known fourth order Numerov t...

The parabolic or forward scattering approximation has been used extensively in the study of wave propagation. This approximation is combined with a gaussian white noise approximation for waves propagating in a random medium. The validity of this approximation is proved for stratiied weakly uctuating random media in the high frequencies regime. The limiting distribution of the wave eld is charac...

In this paper, we give existence and uniqueness results for backward stochastic diierential equations when the generator has polynomial growth in the state variable. We deal with the case of xed terminal time as well as the case of random terminal time. The need for this type of extension of the classical existence and uniqueness results comes from the desire to provide a probabilistic represen...

Phase sensitive analysis of femtosecond pulse propagation in optical fibers employing frequency resolved optical gating (FROG) is presented and compared to numerical simulations employing a modified cubic nonlinear Schr€ odinger equation (NLSE). Phase information obtained from deconvolution of the experimental traces allows the observation and characterization of specific pulse propagation feat...

A method is developed for using large-order perturbation theory to solve the systems of coupled diierential equations that result from variational solution of the Schrr odinger equation with wavefunctions of product form. This is a noniterative, computationally eecient way to solve self-consistent-eld (SCF) equations. Possible applications include electronic structure calculations using product...

The combination of complex scaling with the (t; t 0) representation of the time dependent Schrr odinger equation J. Chem. Phys. 99, 4590 (1993)] enables the design of the graded-index multimode ber to control the distribution of power among the modes. The diierential modal losses are associated with the imaginary parts of the complex eigenvalues of a complex scaled Floquet type operator. Althou...

The generalized Schrr odinger equation d 2 =dx 2 + F (k) = ikP (x) + Q(x)] is considered, where P and Q are integrable potentials with nite rst moments and F satisses certain conditions. The behavior of the scattering coeecients near zeros of F is analyzed. It is shown that in the so-called exceptional case, the values of the scattering coeecients at a zero of F may be aaected by P (x): The loc...

The large distance behavior of weakly bound three-body systems is investigated. The Schr odinger equation and the Faddeev equations are reformulated by an expansion in eigenfunctions of the angular part of a corresponding operator. The resulting coupled set of e ective radial equations are then derived. Both twoand three-body asymptotic behavior are possible and their relative importance is st...