A non-relativistic model of two-particle decay III. The pole approximation

J. Dittrich, Pavel Exner

Arno Böhm, Hani Kaldass, Sujeewa Wickramasekara

Abstract These Gamow kets span an irreducible representation space for Poincaré transformations which, similar to the Wigner representations for stable particles, are characterized by spin (angular momentum of the partial wave amplitude) and complex mass (position of the resonance pole). The Poincaré transformations of the Gamow kets, as well as of the Lippmann‐Schwinger plane wave scattering states, form only a semigroup of Poincaré transformations into the forward light cone. Their transformation properties are derived. From these one obtains an unambiguous definition of resonance mass and width for relativistic resonances. The physical interpretation of these transformations for the Born probabilities and the problem of causality in relativistic quantum physics is discussed.

M. Parkinson

B. M. Garraway

An approach to the decay of a two-state quantum system coupled to a resonant environment is developed in terms of exact (nonperturbative) master equations. Starting from a quantum optical model of a two-level system coupled to a heatbath, it is shown that the effect of the bath can be replaced by one or more pseudomodes. This description is valid for a wide class of analytic density-of-state functions and it leads to exact master equations which fully describe the non-Markovian decay of the quantum system without the use of perturbation theory, the Born approximation, or the Markov approximation. Two examples are given: a simple model of a density-of-states gap which has two poles, and a non-Lorentzian resonance.

John R. Fanchi

Samuel D Lindenbaum

Failure of the classical theories wave packets wave functions and probability Schrodinger's Equation quantum mechanical operators Schrodinger's Equation with forces continuous spectrum Eigensolutions the harmonic oscillator three-dimensional problems matrices matrices in different representations approximate methods I applications of WKB method alpha decay approximate methods II continuous spectrum perturbation approximate methods III spin and spinors fine structure of the hydrogen atom anomalous Zeeman effect assemblages of identical particles the Dirac Equation non-relativistic limits of the Dirac Equation Dirac operator and wave function transformations negative energy solutions - positron theory relativistic theory of Coulomb scattering Compton scattering.