0000000000214275
AUTHOR
Gy. I. Szász
Zur Begründung eines Variationsprinzipes für zerfallende Systeme
Taking into account the circumstance that the decay of an unstable microscopic system into two fragments is established by the counting of one of the decay products in a detector, the observed exponential decay law then asserts only knowledge of the spatiotemporal behaviour of the probability density (and therewith knowledge of the decaying state) at a large finite distance from the site of decay. We therefore formulate a variational principle, of which stationary functions show this decay behaviour. In addition to the resonant wave functions there are also solutions of the variational principle, which decrease exponentially with increasing distance, i.e., functions which could be used to d…
Zu notwendigen Resonanzkriterien im station�ren Einkanal-Fall
First will be exhibited, for the stationary case, a connection between the probability, to find a particle in the region of interaction, and the derivative of the scattering phase shift for the momentum. From the idea, that in stationary scattering a resonance is linked with an appreciable increase of this probability, one obtains new and quantitative criteria for the behavior ofδl(k). For instance, the nonresonant behavior can be characterised by the condition 2kdδl(k)/dk<1. The maximum of probability for the particle to be in the region of interaction, is considered in accordance with the criterium of maximal change of the phase shift, as a function ofk. This characterises the location of…
Zerfallende Zustände als physikalisch nichtisolierbare Teilsysteme
Presently the investigations of decaying quantum mechanical systems lack a well-founded concept, which is reflected by several formal difficulties of the corresponding mathematical treatment. In order to clarify in some respect the situation, we investigate, within the framework of nonrelativistic quantum mechanics, the resonant scattering of an initially well localized partial wave packet ϕl(r, t). If the potential decreases sufficiently fast for r ∞, ϕl(r, t) can be expressed at sufficiently long time after the scattering has taken place, as ϕl(r, t) = I(r, t) + ∑ Niϕl(Ki, r) exp {–iKi2t/2M} × Θ(ki – γi – Mr/t), ϕl(Ki, r) being the resonant solution with complex “momentum” Ki = ki – iγi. …