Chem_370_Handout_01_25_08 - _ CHM 370 Handout Four...

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Unformatted text preview: _ CHM 370 Handout Four Parallels Between Classical and Quantum Mechanics - ' - _ classical memes What is the central quantity The system trajectory . . The system wavefimction X0)? _ r,(t' ..'., rN -‘}‘(r1,...,-rN,t). 'Whatis the equation of ' ' Newton's equation (F = ma). ' The time-dependent motion for X (t) ? Schrodinger equation. What are the possible initial All real values of the particles' All well-behaved complex conditions? ' positions and momenta fin-lotions ‘P(rl,...,rN,r), ’1,"qu which are normalized and are in accord with the system's boundary conditions. By solving the time-dependent Schrodinger equation for a specific initial wave fiinction . ‘Po'lv'wrN’fl' An infinity of system wavefimctions occur, since initial wavefimction generates a unique time—dependent wavefimction ‘P(r,,...,rN,t); ' also-normalized and in Word with the system's boundary conditions. By solving Newton's equation (F = ma) for a specific set of initial-conditions 7161-": Fire)- An infinity of system trajectories occur, since each each set of initial conditions generates a unique trajectm'y 13(1), ..., rN How is X (t) generated? _ How many X (t) ’5 occur? How are observables _ predicted Their values A(t) are 'Their probability distributions from X0)? I determined fi'om the system 114.1) are detemlined from trajectory. the system wavefimction._ How-is the system state The classical state is specified The quantum state is specified specified? by the trajectory ' by the wavefimction 7 = 13(1), ._.., 5(1) since it ‘I’(r,,...,rN,t) since it detennines the values of all determines the probability system observables. distributions for all system : observables. An infinity of quantum states are possible; since each ' wavefiinction determines a uniqUe set of probability distributions for the system observables, and hence specifies a unique quantum An of classical states are possible; "since each "trajectory determines a unique .set' of values for the system ' observables, and hence specifies a unique classical state. How many system states are possible? .- smaooo 3. 1 A33, 3.; ham. 8 on. 80%2 fits Gomudmunvhvwmmu UEOUQW 33% ES Eb Eb EOE E _ . a E gondofifisfi , _ _ , ma 8.03.335, Eu." 2: B 8:833:52 A83; _ “a; b b 3338 x0388 w ac nofiamzmmfisg c2655 mesonsm . mod—S30 ermEoD wuoomm . quEoO EEmEO HOW Hafifiam :03230 Bougomo H8588 080m Ah Enfifi ...
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This note was uploaded on 06/27/2008 for the course CHEM 370 taught by Professor Oldsleepyman during the Fall '08 term at Purdue University-West Lafayette.

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Chem_370_Handout_01_25_08 - _ CHM 370 Handout Four...

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