Indeterminacy For Mixed States
We have described indeterminacy for a quantum system which is in a pure state. Mixed states are a more general kind of state obtained by a statistical mixture of pure states. For mixed states the "quantum recipe" for determining the probability distribution of a measurement is determined as follows:
Let A be an observable of a quantum mechanical system. A is given by a densely defined self-adjoint operator on H. The spectral measure of A is a projection-valued measure defined by the condition
for every Borel subset U of R. Given a mixed state S, we introduce the distribution of A under S as follows:
This is a probability measure defined on the Borel subsets of R which is the probability distribution obtained by measuring A in S.
Read more about this topic: Quantum Indeterminacy
Famous quotes containing the words mixed and/or states:
“Where might is mixed with wit, there is too good an accord in a government.”
—Elizabeth I (1533–1603)
“It may be said that the elegant Swann’s simplicity was but another, more refined form of vanity and that, like other Israelites, my parents’ old friend could present, one by one, the succession of states through which had passed his race, from the most naive snobbishness to the worst coarseness to the finest politeness.”
—Marcel Proust (1871–1922)