Skip to main content
Engineering LibreTexts

1.22: A Summary of Operators

  1. Last updated
  2. Save as PDF
  • Page ID
    50123

    • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    Note there is no operator for time.

    Table \(\PageIndex{1}\): All the operators used in this class.

    Position \(\hat{x}\) x Energy \(\hat{E}\) \(i\hbar\frac{d}{dt}\)
    Wavenumber \(\hat{k}\) \(-i\frac{d}{dx}\) Potential Energy \(\hat{V}\) V
    Angular Frequency \(\hat{\omega}\) \(i\frac{d}{dt}\) Kinetic Energy \(\hat{T}\) \frac{\hat{p}^{2}}{2m}
    Momentum \(\hat{p}\) \(-i\hbar\frac{d}{dx}\) Hamiltonian \(\hat{H}\) \(\frac{\hat{p}^{2}}{2m}+\hat{V}\)

    This page titled 1.22: A Summary of Operators 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.