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Physics LibreTexts

1.8: Using Bras to pick Kets

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

One of the most useful algebraic tricks in quantum mechanics is to multiply a sum of terms by a complex conjugate wavefunction, and integrate the product over all space. Orthogonality often means that this procedure can be used to ‘pick’ a single term from the sum. In Dirac notation this procedure simply becomes applying im|.

For example, if we have an expansion of a mixed state Φ in eigenstates in: ˆH|Φ=nˆH|inin|Φ, we can remove the sum by im|:

im|ˆH|Φ=im|nˆH|inin|Φ=Emim|Φ

This works because im|ˆH|in=Emδnm; it is analogous to taking components of a vector.


This page titled 1.8: Using Bras to pick Kets is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Graeme Ackland via source content that was edited to the style and standards of the LibreTexts platform.

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