Collision of a Free Particle with a Potential Field

S. P. Khare

Klaus Mølmer

Quantum scattering of particles in a periodic potential differs from scattering of free particles because of the non-trivial relation between energy and momentum, and because the potential can extract or provide momentum in the form of integer multiples of the lattice momentum vectors. In this paper, we study solutions for the single-particle dynamics in periodic potentials in one and more dimensions, and we identify the possible final states for various collision processes. This analysis leads to an interpretation of recently performed experiments on four-wave mixing and collisions of Bose–Einstein condensates and to predictions for further collision experiments.

Roy J. Glauber

The Quantum Mechanical Theory of Collis3ions. I»-In the present course we shall consider the quantum mechanical treatment of problems of particle interactions in which at least one of the particles is unbound and therefore able to travel large distances freely.In effect such particles are able to communicate the results of their interaction directly to macroscopic detection apparatus* The interpretation of the resulting data is in general the most direct way of forming conclusions about the interactions.A considerable variety of physical phenomena involves unbound particles» Among the simplest are scattering processes ;in particular the deflection of particles from a collinated beam.More general collision processes which induce reactions of various sorts also lie within the class we shall examine, Our chief concern willbe with the means of solving problems in which well-defined models have been postulated to describe the basic interactions.We shall restrict ourselves, in fact, to the treatment of fairly simple models, and shall discuss a number of approaches to the problems they raise.We begin by discussing the scattering of particles by a simple potential field, fixed in space» The problem of two free particles with a potential between them of course assumes this form in the center-of-mass system.By imagining that a beam of particles of constant strenght is at all times being scattered by the potential, we cay seek to describe the situation with the stationary-state Schrb'dinger equation.

G. F. Drukarev

Benjamin W. Schumacher, Michael D. Westmoreland

В. А. Алексеев, D. D. Krylova

We present exact time-dependent solutions of the Fokker–Planck equation including the collisional term, which describes the influence of the laser field and collisions with the surrounding gas on the temporal behavior of the distribution function of cooled particles in the last stage of the cooling process. These solutions allow us to estimate the influence of collisions on the limiting temperature of free particles and trapped ions.