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1.13: Bra and Ket Notation

  • Page ID
    50110
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    Also known as Dirac notation, Bra and Ket notation is a convenient shorthand for the integrals above.

    The wavefunction is represented by a Ket:

    \[ \psi(x) \rightarrow |\psi\rangle \nonumber \]

    The complex conjugate is represented by a Bra:

    \[ \psi^{*}(x) \rightarrow \langle \psi| \nonumber \]

    Together, the bracket \( \langle \psi| \psi \rangle\) (hence Bra and Ket) symbolizes an integration over all space:

    \[ \int^{+\infty}_{-\infty}\psi^{*}(x)\psi(x) \rightarrow \langle \psi| \psi \rangle \nonumber \]

    Thus, in short form the expectation value of x is

    \[ \langle x\rangle = \frac{\langle \psi|x|\psi \rangle}{\langle \psi|\psi\rangle} \nonumber \]


    This page titled 1.13: Bra and Ket Notation is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Marc Baldo (MIT OpenCourseWare) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.