l20 - F max 5:7 iécéuj'7 if" f" ‘ Quantum...

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Unformatted text preview: F? max 5:7 iécéuj: '7 if": _. f " ‘ Quantum Harmonic Oscillator: Wavefunctions The Schrodinoi er agitation for a hannonic oscillator may be solved to give the wavefunctions illustrated below. potential and wavefunctions ' ' w? 0 For the simple harmonic oscillator (the spring) the potential is V = $ka (1) can 2 fl we 2 27rf [2) m We used the uncertainty prinicple to estimate that the particle at the bottom of the well oscillates over a length scale L = ($91“ (3) and the classical oscillation frequency is The lowest energies are The lowest wave functions are 5‘ H where ya; (8) _ _q_______mmm__Lm 3M (Eng-mm m kimoémw Mm; I . ._._. ._._ m. ._.... w... ....._. w _ ..,.__,.... . - ’2- . — _— _._........_. _. _ __ M ___ m ___ _F____- .. 4b.”. w q+ '- 1: u u ._.u 2mm __ M.“ .. _m?1. . _ _._ _ . {:ijth Chewy: ~_ J(:9 _nglmwsigwkeés var?ng H. II= >3. _- _____________ ._ ._ _....._ _..__ -_. ._._ L...— ___ Ema. chasm». a. “fighting 04 mm“; m fl, 3M Quad Mew; h h m W1st imfi / {>05 w w w _ '''' M m """"""""""" "a - __________________ ._ .09; .+ .Lka- m><1 1H ~= 6?; 2:“?ka 533?} 2 ,_ :Eélgg a; " 3m... m5 ‘7 ...... j {5 £7“: a h w m. M 9‘3: m _ m f. m “hawk m I“ , m w- u. i ___m__ __ ________ __ 'J. x. .1. 7E,L 7* = t: U w W. *. “be a Lay) ____ _;;J:__/u’ o. * M m m 2. 5 w Jr “Ex “@553 w ....... «5672;{23%) $76; >_ @x "fifl" H w PM " “ ,.._ m M W "Li """" 1' f w ..... .. :Qcm will @fpmck Q 055 >.£ “‘9 :0 , m 3e,__ ...
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l20 - F max 5:7 iécéuj'7 if" f" ‘ Quantum...

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