{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Chem_370_Handout_01_25_08

# Chem_370_Handout_01_25_08 - CHM 370 Handout Four Parallels...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

{[ snackBarMessage ]}

### Page1 / 2

Chem_370_Handout_01_25_08 - CHM 370 Handout Four Parallels...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online