Temporally continuous approximation of temporally quantized statistical operators

Any temporally-quantized statistical operator characterizing a dynamically isolated and localized non-relativistic quantum system which evolves strictly irreversibly can be approximated quite well for many purposes by one in which its intrinsic discrete overall time lapses are merely replaced by an appropriate single continuous temporal parameter. Each such approximation differs very little from its original because of a small total squared difference of the two which is found to exist at all times. It is readily produced from any statistical operator which is a solution of the pertinent von Neumanʹs equation of motion. The approximation satisfies a temporal differential equation similar in some respects to that ascribed conventionally to a subsystem interacting with the remainder of an otherwise isolated quantum system and to that proposed recently imposing an intrinsic decoherence on the evolutionary behavior of such systems, but differs fundamentally from both. Several examples illustrate the applicability and limitations of the approximation.