Energy-Lifetime Relations

M. Bauer, Pier A. Mello

A new formulation of the uncertainty relation of position and momentum, and of energy and time, is presented. The connection between the lifetime of excited states and the energy width of these states, which does not follow from the usual uncertainty relation, is shown to be a consequence of the expression here derived.

W.J. Caspers

M. Bauer, Pier A. Mello

A new formulation of the uncertainty rela- tion of position and momentum, and of energy and time, is presented. The connection between the lifetime of excited states and the energy width of these states, which does not follow from the usual uncertainty relation, is shown to be a consequence of the expression here derived.

Dale M. Grimes

M. Moshińsky

The purpose of this paper is to discuss two forms in which the time–energy uncertainty relation can appear. One of them concerns the time of preparation of a given state and the other the lifetime of compound systems. Both will be illustrated here through exactly solvable examples. The first one will be the opening and subsequent closing of a shutter on which we have an incident beam of particles. This problem shows a diffraction-in-time effect closely connected with the first type of time–energy uncertainty relation. The second will be the decay of a compound state described through a schematic R matrix formalism. There one can clearly see the transition between the time–energy uncertainty relation as associated with the interval in which the decay process has been in operation, and as associated with the lifetime of the compound state.

Pieter Kok