On a generalization of the concept of state property system

Diederik Aerts, Didier Deses

K. Kong Wan

This chapter sets out some general physical properties of classical systems which are divided into discrete and continuous: Discrete systems These are systems of discrete point particles. The specific structure of classical mechanics is presented with position, linear and angular momenta serving as basic observables. Continuous systems These systems are illustrated by a vibrating string. Continuous systems have different kinds of properties and observables, e.g., wave properties. In particular we have discussed: Description of states by solutions of the classical wave equation. The concept of eigenfunctions with orthonormality property and their superposition and interference. The concept of a complete set of states.

D.J. Moore

Naila Amir, Shahid Iqbal

Abstract A generalized scheme for the construction of coherent states in the context of position-dependent effective mass systems has been presented. This formalism is based on the ladder operators and associated algebra of the system which are obtained using the concepts of supersymmetric quantum mechanics and the property of shape invariance. In order to exemplify the general results and to analyze the properties of the coherent states, several examples have been considered.

Bart D’Hooghe

Diederik Aerts

The aim of this article is to represent the general description of an entity by means of its states, contexts and properties. The entity that we want to describe does not necessarily have to be a physical entity, but can also be an entity of a more abstract nature, for example a concept, or a cultural artifact, or the mind of a person, etc..., which means that we aim at very general description. The effect that a context has on the state of the entity plays a fundamental role, which means that our approach is intrinsically contextual. The approach is inspired by the mathematical formalisms that have been developed in axiomatic quantum mechanics, where a specific type of quantum contextuality is modelled. However, because in general states also influence context -- which is not the case in quantum mechanics -- we need a more general setting than the one used there. Our focus on context as a fundamental concept makes it possible to unify `dynamical change' and `change under influence of measurement', which makes our approach also more general and more powerful than the traditional quantum axiomatic approaches. For this reason an experiment (or measurement) is introduced as a specific kind of context. Mathematically we introduce a state context property system as the structure to describe an entity by means of its states, contexts and properties. We also strive from the start to a categorical setting and derive the morphisms between state context property systems from a merological covariance principle. We introduce the category SCOP with as elements the state context property systems and as morphisms the ones that we derived from this merological covariance principle. We introduce property completeness and state completeness and study the operational foundation of the formalism