HeisenbergUncertaintyPrinciple 2008-10-16 13:37:46 2008-10-16 13:54:09 Law quantum uncertainty identity operator Heisenberg uncertainty principle quantum theory % 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{Heisenberg Uncertainty Principle in Quantum theories:} If X and P are, respectively, the coordinate and conjugate momentum quantum operators then they satisfy the Heisenberg non-commutation/ 'uncertainty' relation, or the \emph{Heisenberg Uncertainty Principle}: $$[X,P] \geq i\hbar I,$$ where the identity operator $I$ is employed to simplify notation. Stated in words, in quantum physics, the \emph{Heisenberg uncertainty principle} says that one cannot simultaneously measure with any desired precision both the position and momentum of a quantum particle; thus, ``locating a particle in a small region of space makes the momentum of the particle uncertain, and conversely, measuring precisely the momentum of a particle makes the position uncertain--in inverse proportion to the precision of the particle momentum measurement''. The principle applies also to energy and time, where it takes however a somewhat different form in quantum mechanics and QFT. More generally, it applies to many, but not all quantum operators, as there are certain pairs of quantum operators that do commute--those that belong to the same set of eigenvalues. \textbf{Note:} A quantum `particle' is also subject to the de Broglie {\em wave-particle duality} principle, which establishes the relation between the associated wavelength and the momentum of a quantum particle.