A new method in the quantum theory of decaying states

Takashi Nakamura, Adrian C. Ottewill, Shin Takagi

A.P. Grécos

Sture Nordholm, George B. Bacskay

The aim of this work is to provide a new conceptually and practically useful method of obtaining the time development and particularly the decay of quantum states initially localized on a domain with dynamically open boundaries. A projection operator derivation and a Markoffian approximation is used to obtain an effective Hamiltonian capable of describing the dynamics on the open domain. The basic algebra is implemented for one dimensional systems and a series of test calculations presented which serve to verify the validity of the approximations and illustrate the accuracy of the new procedure. The absorbing boundary method developed here bears some resemblance to the optical potential methods and the Feshbach projection scheme used in scattering theory and can be applied to dissociation and ionization processes as well as to scattering processes.

Gang Hu, Ilya Prigogine

E. A. Boldt, Guido V. Sandri

A new method in the theory of unstable particles is introduced. It is applied in this paper to a simple model to show how the exponential regime of the decay can be isolated systematically. It is further shown that our method prescribes the precise conditions to which the initial wave function must be submitted for this exponential decay to ensue. The prescription of these conditions constitutes in fact a definition of an "unstable particle" in quantum theory.

Gennady Mil’nikov, António J. C. Varandas

The paper presents a new semiclassical theory of multidimensional tunneling and its application to the decay problem. A simple semiclassical expression for the decay rate constant is derived in terms of complex valued family of classical trajectories in the decay valley while the algebraic form of the family in the tunneling region is found by means of classical canonical perturbation theory. This provides a tool to analytically continue the classical trajectories into the decay valley, with a numerical illustration of such a continuation being done for a model 2D decay rate problem. The calculated results for the rate constant are found to be in good agreement with the exact ones for the high levels where the suggested perturbative treatment is applicable. It is also shown that the formulated theory can be directly compared with a previously proposed hopping method which gives a way to examine the accuracy of the latter without exact quantum calculations.