DiracNotation 2006-05-30 11:18:21 2006-05-30 11:25:49 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 Dirac notation 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 ${\phi}$.