DiracNotation 2006-05-30 11:18:21 2009-01-30 15:50:05 Topic This is a contributed topic entry in progress. % 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 \subsection{Introduction} \subsection{Non-Abelian Observable (Clifford) Algebra} \subsection{Dirac relativistic quantum field equations} \subsection{Dirac delta and $<bra>c<ket>$ notations} Dirac notations (or ``bra-ket'' notation as commonly known in physics) is used to represent quantum states in quantum mechanics. It was invented by Paul Dirac and since then has been a prefered way of notation in quantum mechanics. The notation denotes the ``ket'' vector defined as $|{\psi}>$ and its transpose vector is defined as $<{\phi}|$ or ``bra'' vector. Then ``bra-ket'' is defined as the inner product of the two which is noted as $<{\phi}|{\psi}>$. Dirac notation also satisifies following identities: $<{\phi}|{\omega}|{\psi}>{\equiv}<{\phi}|{\omega}{\psi}>$\\ $<{\phi}|{\psi}>{\equiv}\int_{-{\infty}}^{\infty} \widetilde{\phi} {\psi} dx \quad$\\ Where $\widetilde{\phi}$ is complex conjugate of ${\phi}$. \begin{thebibliography}{9} \bibitem(PAMD68) Paul A.M. Dirac. 1968. {\em Principles of Quantum Mechanics}, Cambridge University Press, Cambridge, UK \end{thebibliography}