Announcements:• Final Projects – give me your 1stpass ideas today• Ass. #6 due Friday 3/3; no class so drop it off in my office 408 CB or e-mail it to me Today:• discuss final projects• comments on WS#5 and expectation values• begin Worksheet #6 (finish Wed.)2/27/06Team AssignmentsTeam Name Job (#6) (from #5) 1 Eric speaker recorder1 Dave recorder speaker1 Sarah speaker analyst1 Hongping analyst manager2 Simeon speaker analyst2 Marielle analyst manager2 Alec manager recorder2 Will recorder speaker3 Sean recorder manager & speaker3 Joe manager & speakeranalyst3 Daniel analyst recorderxxxxxxxxxxxxxxxx"We choose to examine a phenomenon which is impossible, absolutelyimpossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery." R. P. Feynman, Lectures on PhysicsABP=PA+PBYoung’s 2-Slit Experiment with ParticlesNePVoted the most beautiful experiment in physics (Physics World 2002)Now with ElectronseP≠PA+PBunobservedABP=PA+PBobservedTeam Name Job (#6) 1Eric speaker1 Dave recorder1 Sarah speaker1 Hongping analyst2Simeonspeaker2 Marielle analyst2 Alec manager2 Will recorder3 Sean recorder3 Joe manager & speaker3 Daniel analystAssignment #6:• skip 1stpage, we’ll discuss together• go through Model #1 & stop after #9 for discussion• do not do Exercises in class unless your group is ahead & waiting (do them on your own for further edification)• we’ll finish (at least) through activity 8 todayfrom D. A. McQuarrie, Quantum Chemistry (University Science Books, 1983)from biography of Michael Kasha in The Spectrum 18, 4 (2005)Postulate II. Every dynamical variable (or physical observable) is represented by a corresponding linear operator. Postulate III. When a dynamical variable A is measured (without experimental error), there are only certain possible values that may be obtained. These values are the eigenvalues ai of the operator Aˆ as given by iiiaAφφ=ˆ where φi is one of the eigenfunctions of the operator Aˆ representing the dynamical variable A. When a system is not in an eigenstate of the observable A of interest, it is possible to say much more than simply the result of a measurement must be one of the eigenvalues of the operator Aˆ. It is a property of observable operators Aˆ that the set of all eigenfunctions of such an operator {φi(τ)} forms a complete basis set with which any wavefunction in of the system ψ(τ) may be expanded: ∑=iiic )()(τφτψ (0-1) “τ” here denotes all of the coordinates of the system. The coefficients ci in expansion 0-1 provide the relative probabilities P(φi) that a measurement of A will find the system in the eigenstate φi and the measurement of A will therefore yield the value ai in the following manner: ∫∗∗=ττψτψφdccPiii)()()( (0-2) If a measurement is made on a collection of systems all in the state ψ(τ) the average or expectation value of the observable A is given by: ∫∫∑∗∗=>=<ττψτψττψτψφddAaPAiii)()()(ˆ)()(
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