pure state

The term pure state refers to several related concepts in physics, particularly quantum mechanics and in functional analysis. In quantum mechanics a pure state S of a quantum system is a state represented by a density operator which cannot be decomposed as a randomization of two statistically different statistical ensembles. Mathematically this means S is an extreme point in the set of states. Such states are given in Dirac bra-ket notation by

S = | \psi \rangle \langle \psi |

In the density operator formalism, a pure state is an idempotent transformation, following the properties of projection operators

\rho = \rho^2

A pure state on a C*-algebra A is a state which is an extreme point of the set of all states on A. By properties of the GNS construction these states correspond to irreducible representations of A. The states of the C*-algebra of compact operators K(H) correspond exactly to the density operators and therefore the pure states of K(H) are exactly the pures states in the sense of quantum mechanics.

<< Previous

Word Browser

Next >>

hornpipe
quahog
set (disambiguation)
uss ponchatoula (ao 148)
northwood (tv series)
blohm & voss bv 40
inglfur arnarson
set dance
grignard reagent
signaling gateway
focke wulf fw 189

step dance
slip jig
soft phone
streamliner
johnstown flood
propafenone
unital
slipstream
positive linear functional
positive element
henschel hs 123

callmanager
heinkel he 51
list of films: u.s. box office bombs
mg 17 machine gun
hawaii's story by hawaii's queen
john forbes (general)
state (functional analysis)
chant
messerschmitt me 263
southern strategy
t pyxidis

extreme point
john forbes
superstition mountains
160 (number)
list of national parks of japan
170 (number)
180 (number)
nbar
rgen (district)
190 (number)
j.p. morgan chase tower, dallas