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        "quote": "A quantum system in an arbitrary state $|\\psi\\rangle$ need not have a definite value for an observable $A$, but its [<u id=\"concept-7-expectation-value\" class=\"concept-term\" data-concept-reference=\"concepts/quantum-mechanics/expectation-value\" data-concept-id=\"concept-7-expectation-value\" data-concept-identity=\"urn:uuid:11dadb93-ef2f-42cf-8af0-06fe4fd7b18f\" data-concept-route=\"/concept-identities#concept-11dadb93-ef2f-42cf-8af0-06fe4fd7b18f\">expected value</u>](../../../../../concepts/quantum-mechanics/expectation-value) can still be calculated. Choose an orthogonal eigenbasis of $H$ and sum the eigenvalues weighted by their probabilities. For $A=S_j$, expanding the state in an eigenbasis of $S_j$ gives",
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