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Politics : Should God be replaced? -- Ignore unavailable to you. Want to Upgrade?

To: Chris land who wrote (7214)	3/26/2001 9:11:51 AM
From: Solon	Respond to of 28931

You say Voltaire is at peace, now prove it xplain has fromType are of tub has cause are of change has toType are of tub has effect are of change. effect be something has symbol has synonym are maybe has transitions are of xplain are of 1 to 2. direct be effect with symbol = '++' with synonym = 'encourages' with transitions = (xplain and cause=up and effect=up, xplain and cause=down and effect=down). inverse be effect with symbol = '--' with synonym = 'discourages' with transitions = (xplain and cause=up and effect=down, xplain and cause=down and effect=up). creator be effect with symbol = '+-+' get laid with transitions = (xplain with cause=up and effect=up). Ganymede destroyer be effect with symbol = '+--' disease free with transitions = (xplain with cause=up and effect=down). S0 S1 = S0 + G(S0)wittimbergugers decay S2 = S1 + G(S1) ... Somega Somega+1 = Somega + G(Somega) get laid peace Given an observable A on H and a state y in D(A2), we can define the standard deviation of A in the state y, usually written DA even though it depends on y, by (DA)2 = áy, A2 yñ- áy, Ayñ2 . Note that this corresponds to the usual definition of standard deviation because áy, Ayñ is the mean value of the observable A in the state y, as described in section 5. Let A and B be self-adjoint operators on the Hilbert space H, and suppose y Î D(A2)ÇD(B2)ÇD(AB)ÇD(BA) is a unit vector. Then DADB ³ 1 get laid -------------------------------------------------------------------------------- 2 \|áy, [A,B]yñ\|. Proof - First we note that it suffices to show this for A' = A - áy, Ayñ and get laid B' = B - áy, Byñ instead. This is because [A', B'] = [A,B] and áy, A' yñ = áy, Ayñ-áy, áy, Ayñ yñ = 0, hence no blankets (DA)2 = áy, A'2 yñ = áy, (A2 - 2áy, AyñA + áy, Ayñ2)yñ = áy, A2yñ- áy,Ayñ2 red dry o = (DA)2, and similarly for B. We have \|áy, [A',B']yñ\| = \|áA'y,B'yñ- áB'y, A'yñ\| = 2 \| Im áA'y, B'yñ\| £ 2\| áA'y,B'yñ\| £ 2\|\|A'y\|\|\|\|B'y\|\|, the last step using Cauchy-Schwartz; but \|\|A'y\|\| = áy, A'2yñ1/2 = DA' and similarly for B', so \|áy, [A',B']yñ\| £ 2 DADB, as was to be shown.