We consider the Schrr odinger equation for a class of two-level atoms in a quasi-periodic external eld for large coupling, i.e., for which the energy diierence 2 between the unperturbed levels is suuciently small. We show that this equation has a solution in terms of a formal power series in , with coeecients which are quasi-periodical functions of the time, in analogy to the Lindstedt-Poincar ...

Wavelet applications to date have been dominated by signal and image processing. While perhaps not immediately obvious as a means of solving diierential equations, the growing body of literature in this area indicates that wavelets have a role to play here, too. Particularly attractive is their multilevel structure which leads to the possibility of data compression. In this paper we give some o...

Using the nonlinear differential equations governing the motion of a fluid-filled and prestressed long thin elastic tube, the propagation of nonlinear waves near the marginal state is examined through the use of reductive perturbation method. It is shown that the amplitude modulation near the marginal state is governed by a generalized nonlinear Schr€ odinger (GNLS) equation. Some exact solutio...

We construct the action-angle variables of a classical integrable model dened on complex projective phase space and calculate the quantum mechanical propagator in the coherent state path integral representation using the stationary phase approximation. We show that the resulting expression for the propagator coincides with the exact propagator which was obtained by solving the time-dependent Sc...

A few numerical methods for linear evolution equations are developed and analyzed in this paper. These fourth order methods allow large step sizes for highly oscillatory equations when the evolution operators vary slowly in time. The methods are also conservative for equations such as the Schrr odinger equation, where the evolution operator is skew-selfadjoint.

Cheap and easy to implement fourth-order methods for the Schrr odinger equation with time-dependent Hamiltonians are introduced. The methods require evaluations of exponentials of simple unidimensional inte-grals, and can be considered an averaging technique, preserving many of the qualitative properties of the exact solution. INTRODUCTION. In this work we present new fourth-order geometric

A detailed list of postulates is formulated in an algebraic setting. These postulates are suucient to entail the standard time evolution governed by the Schrr odinger-or Dirac equation. They are also necessary in a strong sense: Dropping any one of the postulates allows for other types of time-evolution, as is demonstrated with examples. Some philosophical remarks shall hint on possible further...

We derive radiative transport equations for solutions of a Schrodinger equation in a periodic structure with small random inhomogeneities. We use systematically the Wigner transform and the Bloch wave expansion. The streaming part of the radiative transport equations is determined entirely by the Bloch spectrum, while the scattering part by the random uctuations.

Two ultracold atoms moving in a trap interact weakly at a very short distance. This interaction can be modeled by a properly regularized contact potential. We solve the corresponding time{independent Schrr odinger equation under the assumption of a parabolic, spherically symmetric trapping potential.

Homoclinic varieties play a crucial role in the dynamics of perturbations of the focusing Nonlinear Schrr odinger equation (NLS). We undertake a Mel'nikov analysis to investigate the possibility of persistence of transversal homoclinic orbits for a conservative perturbation of the NLS.