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# 3.2: Operators


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

$\hat{H} ψ(x,t) = − \dfrac{\hbar^2}{2 m} \dfrac{∂^2}{∂ x^2} ψ(x,t) + V(x) ψ ( x , t ) . \label{3.16}$

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

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 conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.