Recent developments in the time analysis of tunneling processes

Anedio Ranfagni, Daniela Mugnai

V. S. Olkhovsky

Recent developments are reviewed and some new results are presented in the study of time in quantum mechanics and quantum electrodynamics as an observable, canonically conjugate to energy. This paper deals with the maximal Hermitian (but nonself‐adjoint) operator for time which appears in nonrelativistic quantum mechanics and in quantum electrodynamics for systems with continuous energy spectra and also, briefly, with the four‐momentum and four‐position operators, for relativistic spin‐zero particles. Two measures of averaging over time and connection between them are analyzed. The results of the study of time as a quantum observable in the cases of the discrete energy spectra are also presented, and in this case the quasi‐self‐adjoint time operator appears. Then, the general foundations of time analysis of quantum processes (collisions and decays) are developed on the base of time operator with the proper measures of averaging over time. Finally, some applications of time analysis of quantum processes (concretely, tunneling phenomena and nuclear processes) are reviewed.

V. S. Olkhovsky, Erasmo Recami

Some new results are presented and recent developments are reviewed on the study of Time in quantum physics as an observable, canonically conjugate to energy. Operators for the observable Time are investigated in particle and photon quantum theory. In particular, this paper deals with the Hermitian (more precisely, maximal Hermitian, but non-self-adjoint) operator for Time which appears: (i) for particles, in ordinary nonrelativistic quantum mechanics; and (ii) for photons (i.e. in first-quantization quantum electrodynamics). In conclusion, various recent and possible future applications of the time quantum analysis for tunnelling processes, nuclear collisions and systems with (quasi)discrete energy spectra are indicated.

N. G. Kelkar, D. Lozano Gómez, Edgar J. Patiño

Pranab Sarkar

V. S. Olkhovsky, S. P. Maidanyuk

The problem of scattering of a nonrelativistic particle on a nucleus is considered, the interaction potential between which has a spherically symmetrical view. As the further development of the time analysis of processes of tunneling the non-stationary method of the solution of a problem is represented, due to which begins the possibility to describe in a time dependence the propagation (tunneling) of a particle and in details to study this process in an interesting instant or concerning a concrete point of space. At calculating the time parameters the method has shown itself simple and convenient. At finding the expressions for stationary wave functions for problems with an interaction potential, which radial part has more composite view than rectangular, this method is more effective than reference stationary approaches.