Chem120A+Notes+9-10-08 - Chem120A Notes 9/10/08 Different...

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Chem120A Notes 9/10/08 Different versions of the postulates of quantum mechanics Postulate III: “Suppose that A ˆ is an operator corresponding to an observable and that there is a set of identical systems in state s Ψ . Suppose further that s Ψ is an eigenfunction of A ˆ . s a s a A Ψ = Ψ ˆ where a s is a number. Then, if an experimentalist makes a series of measurements of a quality corresponding to A ˆ on different members of the set the result will always be a s . It is only when s Ψ and A ˆ satisfy this condition that an experiment will give the same result on each measurement. Postulate IV: “Given an operator and a set of identical systems characterized by a function s Ψ that is not an eigenfunction of A ˆ , a series of measurements of the property corresponding to A ˆ on different members of the set will not give the same result. Rather, a distribution of discrete results will be obtained, the average of which will be:” τ d d A A Ψ Ψ Ψ Ψ = * *
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This note was uploaded on 09/28/2009 for the course CHEM 120A taught by Professor Whaley during the Spring '07 term at University of California, Berkeley.

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Chem120A+Notes+9-10-08 - Chem120A Notes 9/10/08 Different...

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