Transparent boundary conditions (TBCs) for general Schrr odinger{ type equations on a bounded domain can be derived explicitly under the assumption that the given potential V is constant on the exterior of that domain. In 1D these boundary conditions are non{local in time (of memory type). Existing discretizations of these TBCs have accuracy problems and render the overall Crank{Nicolson nite d...

A density-gradient (DG) model is used to calculate quantum-mechanical corrections to classical carrier transport in MOS in-version/accumulation layers. The model is compared to measured data and to a fully self-consistent coupled Schrr odinger and Pois-son equation (SCSP) solver. Good agreement is demonstrated for MOS capacitors with gate oxide as thin as 21 A. It is then applied to study carri...

The one-dimensional Schrodinger equation is considered for real potentials that are integrable, have nite rst moment, and contain no bound states. The recovery of a potential with support in a right half-line is studied in terms of the scattering data consisting of the magnitude of the re ection coe cient, a known potential placed to the left of the unknown potential, and the magnitude of the ...

Difference Fermi resonance interface modes occur in layered molecular materials when two excitations on one side of an interface differ in energy by an amount that matches approximately the energy of an excitation to which they are coupled on the other side, provided that the mismatch (detuning) is less in magnitude than the non-linear coupling across the interface. Under this resonance conditi...

We present a simple and efficient numerical method for the simulation of the three-dimensional pyramid quantum dot heterostructure. The pyramid-shaped quantum dot is placed in a computational box with uniform mesh in Cartesian coordinates. The corresponding Schr€ odinger equation is discretized using the finite volume method and the interface conditions are incorporated into the discretization ...

We study the pair description of heavy tetraquark systems $|QQ\overline{Q}\overline{Q}?$ in frame a nonrelativistic potential model. By taking two quark pairs $(Q\overline{Q})$ as colored clusters, four-quark Schr\"odinger equation is reduced to two-pair equation, when inner motion inside can be neglected. Taking into account all Casimir scaling potentials between quarks and using lattice QCD s...

The Schrr odinger-Weyl representation of the canonical commutation relation is cir-culary invariant in a sense. Here, as a continuation of 5 , we show the converse.

The authors report a theoretical study on the process of stimulated Compton scattering in close-to-threshold ionization hydrogen molecule with x-ray attosecond radiation by solving time-dependent Schr\"odinger equation nondipole corrections. They show how to control and isolate nondipole-induced nonlinear photoelectron emission adjusting laser parameters molecular alignment.

In this paper, we prove the global well-posedness for focusing, cubic nonlinear Schr\"odinger equation on product space $\mathbb{R} \times \mathbb{T}^3$ with initial data below threshold that arises from ground state in Euclidean setting. The defocusing analogue was discussed and proved Ionescu-Pausader \cite{IPRT3} (Comm. Math. Phys. 312 (2012), no. 3, 781-831).

This paper contains a study of the transmission of a soliton through a slab of nonlinear and random medium. A random nonlinear Schrr odinger equation is considered, where the randomness holds in the potential and the nonlinear coeecient. Using the inverse scattering transform, we exhibit several asymptotic behaviors corresponding to the limit when the amplitudes of the random uctuations go to z...