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1.3: Operators and Observables

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    In addition to position, a full description of a system must contain some implicit information. The abstract bra-ket notation includes this.

    Consider the electric charge. Obviously this is measurable, so it should be associated with an operator \(\hat{Q}\), such that e.g.

    \[\hat{Q}|\Phi \rangle = −e| \Phi \rangle\nonumber\]

    where \(\Phi\) is the wavefunction of an electron. \(−e\) meets all the criteria for a quantum number, and the above equation is obviously a true representation of reality. Thus the meaning of the ket \(|\Phi \rangle\) is broader than a simple spatial function, and operators can also be non-algebraic. This is especially important in particle physics where all manner of quantum numbers appear (isospin, strangeness, baryon number etc. etc.)

    This page titled 1.3: Operators and Observables 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; a detailed edit history is available upon request.

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