On the structure of the three particle collision operator in quantum mechanics

Pierre M. V. Résibois

Pierre M. V. Résibois

Pierre M. V. Résibois

J. T. Lowry, William C. Schieve

The relationship between the collision kernel of the three-body quantum mechanical kinetic equation (quantum version of the Choh-Uhlenbeck equation) and modern scattering theory is examined utilizing the work of Faddeev and Weinberg. Recognizing that the collision kernel is related to the M⊘ller scattering operator it is shown that the collision kernel is “well-defined” for suitable interaction potentials and contains only connected three particle collisions in the sense of Weinberg. The collision kernel is interpreted physically and is shown to contain a generalization of the ordinary Boltzmann collision term to three particle processes plus a distorted-wave-impulse approximation correction to the two particle Boltzmann collision term.

Rostislav V. Vedrinskii

Thomas M. Nordlund, Peter Manfred Hoffmann

Introducing quantum mechanics immediately after considering the issue of cell division and cell-cell recognition, with their associated complex structures and structural changes, is rather shocking. “Continuum” normally refers to the continuous allowed values of energy of a quantum particle once its energy becomes positive. Electrons bound to atoms have negative total energies, indicating they are in bound states. Stationary states of relevance in biophysics usually occur in cases of electrons or protons bound to atoms or molecules. The chapter examines some interesting and apparently complicated cases in photosynthesis and heme proteins. Symmetry is an important concept in both quantum mechanics and in biosystems. Collisions of atoms constantly occur in gases, liquids, and solids. Particle collisions are the bread and butter of particle physics. The discovery of the “Rutherford atom” was made by collision experiments, Rutherford scattering, and first showed that an atom had a small, heavy nucleus surrounded by light electrons.