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:
“The middlebrow is the man, or woman, of middlebred intelligence who ambles and saunters now on this side of the hedge, now on that, in pursuit of no single object, neither art itself nor life itself, but both mixed indistinguishably, and rather nastily, with money, fame, power, or prestige.”
—Virginia Woolf (1882–1941)
“The admission of the States of Wyoming and Idaho to the Union are events full of interest and congratulation, not only to the people of those States now happily endowed with a full participation in our privileges and responsibilities, but to all our people. Another belt of States stretches from the Atlantic to the Pacific.”
—Benjamin Harrison (1833–1901)