QMGreensite_merged
22.4. FORWHOMTHEBELL(’STHEOREM)TOLLS 355 wehavejustseenthattheobserveratdetector 2 cannever,bysimplyobservingone oftheparticles, ...
356 CHAPTER22. THEEPRPARADOXANDBELL’STHEOREM ...
Chapter 23 The Problem of Measurement Iwaspleasedtobeabletoanswerimmediately,andIdid. IsaidIdidn’tknow. MarkTwain Morethansevent ...
358 CHAPTER23. THEPROBLEMOFMEASUREMENT exitstheapparatus,whichisenclosedinablackbox,inaneigenstateofSz(seeFig. 22.2). Wheneverwe ...
23.1. MIXTURESANDPURESTATES 359 andreflectsthefactthatthepurestateψ,unlikethemixture(23.2),isnotreally inoneor theotherstateαz o ...
360 CHAPTER23. THEPROBLEMOFMEASUREMENT Theinterferencetermis <AB>int= ∑ i(=j c∗icj<ψi|A|ψj><φi|B|φj> (23.12) a ...
23.2. THEPROBLEMOFMEASUREMENT 361 aneigenstateoftherelevantobservable,thenthecorrespondingeigenvalueissome- howregisteredbythede ...
362 CHAPTER23. THEPROBLEMOFMEASUREMENT THISISAPURESTATE,NOTAMIXTURE!Amixture,fortheparticle-detector systemwouldbe M= { eitherin ...
23.3. THE”CLASSIC”VIEWS(I):VONNEUMANN 363 23.3 The ”Classic” Views (I): von Neumann ThesimplestanswerwasgivenbyvonNeumann,whourg ...
364 CHAPTER23. THEPROBLEMOFMEASUREMENT oftheobjectinisolationfromtheobserver. Rather,thewavefunctionisacompact representationoft ...
23.5. THEMANY-UNIVERSEINTERPRETATION 365 23.5 The Many-Universe Interpretation 23.6 Non-LocalHiddenVariables: TheBohmThe- ory 23 ...
366 CHAPTER23. THEPROBLEMOFMEASUREMENT ...
Chapter 24 The Feynman Path Integral InclassicalphysicstheEuler-Lagrangeequationsarederivedfromtheconditionthat theaction S[x(t) ...
368 CHAPTER24. THEFEYNMANPATHINTEGRAL Toseehowasumoverpathscomesin,letssupposethatweknewthepropagator, foranyHamiltonian,whenthe ...
369 sothat ψ(x,t+!) = ( 1 + ! i ̄h H ) ψ(x,t)+O(!^2 ) = ( 1 −i ! ̄h V+ i! ̄h 2 m d^2 dx^2 +O(!^2 ) ) ψ(x,t) = e−i!V(x)/ ̄h ( ψ(x ...
370 CHAPTER24. THEFEYNMANPATHINTEGRAL SolvingforA,andrecallingη=x−y,wefinallyhavetofirstorderin!, G!(x,y)= ( m 2 iπ! ̄h ) 1 / 2 ...
24.1. THEFREEPARTICLEPROPAGATOR 371 24.1 The Free Particle Propagator Onemightwonderifthepath-integralformulationisuseful: Isitr ...
372 CHAPTER24. THEFEYNMANPATHINTEGRAL (recallthatx=xN, y=x 0 ),andlet a= m 2 i! ̄h (24.29) Then GT(x,y) = lim N→∞ B−N ∫ dzN− 1 d ...
24.2. STATIONARYPHASEANDTHEFUNCTIONALDERIVATIVE 373 andfinally,usingT=N!,wehaveintheN→∞limit GT(x,y)= √ m 2 πi ̄hT eim(x−y) (^2) ...
374 CHAPTER24. THEFEYNMANPATHINTEGRAL Thisexamplegeneralizesinastraightforwardway δ δf(x) fn(y) = lim!→ 0 (f(y)+!δ(y−x))n−fn(y) ...
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