Bra-Ket Notation #

This section describes the properties and handling of the bra-ket notation proposed by Paul Dirac in 1939.

Operations in Bra-Ket Notation

Operations in Bra-Ket Notation # This article describes how to handle bra-ket notation that appears in quantum mechanics. It focuses on the possible operations rather than providing a detailed explanation of the notation itself. 1. Representation of Functions # $$ \begin{align} \psi(\mathbf{r}) &= \langle\mathbf{r}|\psi\rangle \label{e1}\\ \psi(\mathbf{p}) &= \langle\mathbf{p}|\psi\rangle \label{e2} \end{align} $$ $|\psi\rangle$: Description of a state without using a specific basis1 $\psi(\mathbf{r})$: State description in position representation $\psi(\mathbf{p})$: State description in momentum representation

Position and Momentum Representation of States

The goal of this article is to derive $\langle x|p\rangle = e^{ipx}/\sqrt{2\pi\hbar}$ and understand the transformation between position and momentum representations.