We construct minimum-uncertainty solutions of the three-dimensional Schrodinger equation with a Coulomb potential. These wave packets are localized in radial and angular coordinates and are squeezed states in three dimensions. They move on elliptical keplerian trajectories and are appropriate for the description of the corresponding Rydberg wave packets, the production of which is the focus of...

The number of bound states of the one-dimensional Schrodinger equation is analyzed in terms of the number of bound states corresponding to \fragments" of the potential. When the potential is integrable and has a nite rst moment, the sharp inequalities 1 n+ Pn j=1Nj N Pn j=1Nj are proved, where n is the number of fragments, N is the total number of bound states, and Nj is the number of bound st...

Sharp smoothing estimates are proven for magnetic Schrr odinger semigroups in two dimensions under the assumption that the magnetic eld is bounded below by some positive constant B 0. As a consequence the L 1 norm of the associated integral kernel is bounded by the L 1 norm of the Mehler kernel of the Schrr odinger semigroup with the constant magnetic eld B 0 .

The Shabat equation f 0 (t) + q 2 f 0 (qt) + f 2 (t) ? q 2 f 2 (qt) = ; t 2 R; where and q are parameters, is the simplest self-similar reduction of the so called dressing chain for constructing and analysing exactly solvable Schrr odinger equations. It is also relevant to the study of the q-oscillator algebra in quantum mechanics. The main objective of this paper is to investigate whether the ...

We employ global quasi-steady manifolds to rigorously reduce innnite dimensional dynamical systems to nite dimensional ows. The manifolds we construct are not invariant, but through a renormalization group method we capture the long-time evolution of the full system as a ow on the manifold up to a small residual. For the parametric nonlinear Schrr odinger equation (PNLS) we consider a manifold ...

In a recent paper (1) an idea of Bohm ad Vigier (2) about the possible decay of every initial probability density function (pdf), whose evolution is ruled by the quantum Fokker-Planck equation, toward the quantum mechanical pdf has been discussed in the light of the stochastic mechanics. The causal interpretation of the quantum mechanics (3) is based on the idea that a non relativistic particle...

A framework that naturally uni es smoothing and enhancement processes is presented. We generalize the linear and nonlinear scale spaces in the complex domain, by combining the di usion equation with the simpli ed schrodinger equation. A fundamental solution for the linear case is developed. Preliminary analysis of the complex di usion shows that the generalized di usion has properties of both ...

A new paradigm is discussed in which the discrete facet of physical phenomenology is related to the existence of localized wave solutions (solitons) of a underlying metacontinuum (uniied eld, physical vacuum, etc.) while the action at a distance is a manifestation of the internal stresses in metacontinuum. The latter is considered as thin elastic 3D layer (a shell) in the 4D geometrical space. ...

We study the Schrr odinger equation of a class of two-level systems under the action of a periodic time-dependent external eld in the situation where the energy diierence 2 between the free energy levels is suuciently small with respect to the strength of the external interaction. Under suitable conditions we show that this equation has a solution in terms of converging power series expansions ...

The continuous-space Schr\"odinger equation is mapped to the transverse Ising model while achieving an exponential advantage over classical computers: A step closer efficient simulation of multi-particle systems.