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Physics LibreTexts

3.2: Operators

( \newcommand{\kernel}{\mathrm{null}\,}\)

Notice that in deriving the wave equation we replaced the number p or k by a differential acting on the wavefunction. The energy (or rather the Hamiltonian) was replaced by an ”operator”, which when multiplied with the wave function gives a combination of derivatives of the wavefunction and function multiplying the wavefunction, symbolically written as

ˆHψ(x,t)=22m2x2ψ(x,t)+V(x)ψ(x,t).

This appearance of operators (often denoted by hats) where we were used to see numbers is one of the key features of quantum mechanics.


This page titled 3.2: Operators is shared under a CC BY-NC-SA 2.0 license and was authored, remixed, and/or curated by Niels Walet via source content that was edited to the style and standards of the LibreTexts platform.

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