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Citation bot (talk | contribs) Altered title. Add: issue, arxiv, chapter, chapter-url, bibcode, authors 1-1. Removed or converted URL. Removed parameters. Some additions/deletions were parameter name changes. | Use this bot. Report bugs. | Suggested by Abductive | Category:Quantum measurement | #UCB_Category 38/84 |
→Mathematical description: Fixed typo: it's not a generic arrow (can be mixed up for a limit) but set elements being mapped by a transformation. Tags: Mobile edit Mobile app edit Android app edit App section source |
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===Collapse===
To account for the experimental result that repeated measurements of a quantum system give the same results, the theory postulates a "collapse" or "reduction of the state vector" upon observation,<ref name=GriffithsSchroeter3rd>{{Cite book |last1=Griffiths |first1=David J. |title=Introduction to quantum mechanics |last2=Schroeter |first2=Darrell F. |date=2018 |publisher=Cambridge University Press |isbn=978-1-107-18963-8 |edition=3 |___location=Cambridge; New York, NY}}</ref>{{rp|566|q=to account for the fact that an immediately repeated measurement yields the same result, we are forced to assume that the act of measurement collapses the wave function,}} abruptly converting an arbitrary state into a single component eigenstate of the observable:
:<math> | \psi \rangle = \sum_i c_i | \phi_i \rangle \
|\psi'\rangle = |\phi_i\rangle.</math> where the arrow represents a measurement of the observable corresponding to the <math>\phi</math> basis.<ref>{{Cite book |last=Hall |first=Brian C. |title=Quantum theory for mathematicians |date=2013 |publisher=Springer |isbn=978-1-4614-7115-8 |series=Graduate texts in mathematics |___location=New York |page=68}}</ref>
For any single event, only one eigenvalue is measured, chosen randomly from among the possible values.
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