ObservablesAndStates 2009-02-25 15:59:43 2009-02-25 16:14:27 Definition % this is the default PlanetPhysics preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here \section{Introduction} The notions of observables and states are fundamental to mechanics. In this entry, we shall begin with the conceptual background to these ideas, then proceed to examine how these notions work in classical, statistical, and quantum mechanics. The basis for these notions lies in making numerical measurements on physical systems and comparing the observed values with predicted theoretical values. The value measured will depend on the quantity being measured and upon the initial and boundary conditions imposed on the system. To account for this dependence, we introduce observables and states --- an observable is a mathematical entity in a theory which represents a measurement which can be made on the physical system described by that theory and a state is a mathematical entity which encodes conditions placed on that system. [more to come]