Classical stationary particle distributions in collision processes

Abstract

We study the classical distribution of particles in a collision process. This is the classical analogue to the square modulus of the quantum mechanical stationary continuum wavefunction. We evaluate this distribution in coordinate and momentum space analytically, comparing its similarities and discrepancies with the corresponding quantum mechanical particle density.

Photonic Rutherford scattering: A classical and quantum mechanical analogy in ray and wave optics

“…(11). 13,54 B. Alternate trajectory formulation An equivalent trajectory formulation similar to the one given in reference 48 . The distance r C of closest approach for a repulsive potential for a head-on impact, i.e.…”

A classical interpretation of the off-shell Coulomb transition matrix

“…In this sense, and due to the lack of information on its microscopic details, the scattering process can be analysed by means of a stationary state describing the steady flow of an ensemble. The density of particles n(r) in each point of space can easily be evaluated by studying the deformation of a control volume due to the motion of each particle in the potential field U(r) of the target (Samengo et al 1999).…”

“…At later times t, the control volume δV occupied by this particle changes as shown in figure 2, giving rise to a spatial dependence of the particle density n(r) = δN/δV in the ensemble. After a little algebra, it is possible to eliminate all explicit dependences on the time variable t (Fiol et al 1997, Samengo et al 1999,…”

“…Since the classical ensemble describes a situation where each point r in the coordinate space is associated with a well defined impulse p, the density of particles n(p) in momentum space can be readily evaluated by means of the transformation Up to now, we have been assuming that only one trajectory passes through any given point r, and that the relation r ↔ p is one-to-one. Nevertheless, these assumptions are generally untrue and all possible contributions have to be added (Samengo et al 1999).…”

Autoionization of He atoms induced by partially stripped ion impact

“…These and other studies which concentrated on the nature of some oscillatory structures near the autoionization peak [11,12,17] considered Coulomb-like fully stripped projectiles. However, it is known that partially stripped ions show more complex collision dynamics in single ionizing collisions.…”