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 ϕ l ( r , t ). If the potential decreases sufficiently fast for r → ∞, ϕ l ( r , t ) can be expressed at sufficiently long time after the scattering has taken place, as ϕ l ( r , t ) = I ( r , t ) + ∑ N iϕl ( K i , r ) exp {– i K i 2 t /2 M } × Θ( k i – γ i – Mr/t ), ϕ l ( K i , r ) being the resonant solution with complex “momentum” K i = k i – iγ i . From this heuristic relation one can deduce not only the probability for the creation of unstable particles but also obtain some hints to a connection between decaying states and physically nonisolable partial systems. On the other hand, this connection can perhaps display the inadequacy of attempts which suggest to solve the problem of decaying states within the usual Hilbert space methods.