a Multiple-Time Description of Quantum Mechanical Systems

Ken'ichi Takano

We reconstruct quantum mechanics by introducing "information operators" and excluding the concept of wave functions. Multiple information operators simultaneously describe a single system and continuously develop in time even in the process of a measurement. We also introduce the concept of condensation for a system with many degrees of freedom in a rather general meaning. In terms of the multiplicity of description and the condensation, we explain quantum phenomena including measurements without the collapse of the wave function.

Carlton M. Caves

Measurements distributed in time provide information about a system at more than one time; they cannot be described in terms of the conventional language of a system quantum state evolving in time. This paper, the second in a series, explores connections among various ways of formulating a quantum-mechanical description of time-distributed measurements. The natural formulation, involving a ``sum over histories,'' arises directly from Feynman's rules for combining probability amplitudes. One equivalent formulation uses a standard measurement model, in which the system is coupled to a set of ``measuring apparatuses.'' A second equivalent formulation uses the language of ``effects'' and ``operations.'' Still a third formulation attempts to create a new language of multiple-time states and multiple-time eigenstates.

M. Arık, U. Kayserilioglu, Gökhan Ünel

The particle decay problem in the random-set approach leads naturally to the q -Poisson distribution. Motivated by the fact that in the classical quantum mechanical description of particle decay one ends up with a composite system, we construct a Hilbert space using the eigenstates of the average particle number operator N . In this approach, time is represented by integer multiples of an observation quantum . It is shown that these considerations lead to the redefined q -oscillator and an element of acts like a reversal operator on n time-ordered states.

V. D. Vainshtein