Physics 256: Lecture 2. Physics
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1 Physcs 56: Lctur Intro to Quantum Physcs Agnda for Today Complx Numbrs Intrfrnc of lght Intrfrnc Two slt ntrfrnc Dffracton Sngl slt dffracton Physcs 01: Lctur 1, Pg 1
2 Constructv Intrfrnc Ths wll occur whn th path lngth dffrnc s an ntgral numbr of wavlngths Path dffrnc = = l - l 1 = (1,, 3, 4, ) Physcs 01: Lctur 1, Pg
3 Dstructv Intrfrnc Ths wll occur whn th path lngth dffrnc s a half ntgral numbr of wavlngths Path dffrnc = = l - l 1 = (½, 1½, ½, 3½, ) Physcs 01: Lctur 1, Pg 3
4 Young s Doubl Slt Concpt At ponts whr th dffrnc n path lngth s 0,,,, th scrn s brght. Sngl sourc of monochromatc lght d slts-sparatd sparatd by d At ponts whr th dffrnc n path lngth s,3,, th scrn s dark. D Scrn a dstanc D from slts Physcs 01: Lctur 1, Pg 4
5 Young s Doubl Slt Quanttatv L d d Path lngth dffrnc = d sn Constructv ntrfrnc Dstructv ntrfrnc whr n = 0, or 1, or,... d sn d sn n n 1 Physcs 01: Lctur 1, Pg 5
6 Young s Doubl Slt Quanttatv Scrn vry far away D >> d d sn() y/d y Constructv ntrfrnc Dstructv ntrfrnc d sn n d whr n = 0, or 1, or,... sn 1 n d y d n D y 1 n D Physcs 01: Lctur 1, Pg 6
7 Clckr Quston 1: A laboratory xprmnt producs a doubl-slt ntrfrnc pattrn on a scrn. If grn lght s usd, wth vrythng ls th sam, th brght frngs wll b A. Closr togthr B. In th sam postons. C. Farthr apart. D. Thr wll b no frngs bcaus th condtons for ntrfrnc won t b satsfd. λ rd 650 nm λ grn 500 nm Physcs 01: Lctur 1, Pg 7
8 Dffracton of Watr Wavs -D wavs A watr wav, aftr passng through an opnng, sprads out to fll th spac bhnd th opnng. Ths wll-known spradng of wavs s calld dffracton. Physcs 01: Lctur 1, Pg 8
9 a Dffracton Intrfrnc
10 Dffracton Intrfrnc a a a sn( ) a Whn sn( ) rays 1 and 1 wll ntrfr dstructvly. t Rays and start ½ a apart and hav th sam path lngth dffrnc. Condton to ntrfr dstructvly. 1 st mnmum at sn = /a Physcs 01: Lctur 1, Pg 10
11 Dffracton a Angl through whch sound wavs ar dffractd Physcs 01: Lctur 1, Pg 11
12 Wavlngth and Intrfrnc/Dffracton Effcts Whn lght passs through a larg opnng, t maks a sharp-dgd shadow. Whn th wavlngth s vry small compard to slt sz or sparaton ntrfrnc/dffracton ffcts ar nglgbl sn a Physcs 01: Lctur 1, Pg 1
13 Complx Numbrs Quantum mchancs s most lgantly xprssd usng complx numbrs Complx numbr: a s th ral part of c b s th magnary part of c c a b 1 Physcs 01: Lctur 1, Pg 13
14 Complx Conjugat Complx numbr hav a unqu opraton known as complx conjugaton. Complx Conjugat: Absolut Squar: c a b c * a b Th opraton of rplacng wth vrywhr c Absolut squar s always nonngatv and ral c c a b a b a b Physcs 01: Lctur 1, Pg 14
15 Complx Plan: Complx Plan Absolut Squar (dstanc from zro): c Absolut squar s always nonngatv and ral c c a b a b a b Physcs 01: Lctur 1, Pg 15
16 Innr Product Togthr w can dfn th nnr product 1 u u u 1 w w w u u w w 1 w w u w u w u u w u Physcs 01: Lctur 1, Pg 16
17 Clckr Quston : What s th nnr product of ths two complx vctors <w v>? A. -6+ B C. 4-3 D u 1 E w Physcs 01: Lctur 1, Pg 17
18 Innr Product = Gnralzd Dot Product Two vctors ar orthogonal f thr nnr product s zro u w 0 In quantum mchancs w lk vctors that ar normalzd. 1 Physcs 01: Lctur 1, Pg 18
19 Innr Product = Gnralzd Dot Product Is thr a manng bhnd th nnr product? or s t just a mathmatcal tool? Physcs 01: Lctur 1, Pg 19
20 Th Functon Th functon (Eulr s Formula): cos sn Proprts: cos sn Physcs 01: Lctur 1, Pg 0
21 Clckr Quston 3: What s th complx conjugat of c 1 x? c c 1 x 1 A. 1 x 1 B. c 1 x C. c 1 x D. c 1 x A. Physcs 01: Lctur 1, Pg 1
22 Th Functon What? cos sn Complx oscllatng functon As ncrass from 0 to tracs out a unt crcl n th complx plan wth angl rlatv to th postv ral axs Usful whn w want to dscrb oscllatons or wavs compactly Physcs 01: Lctur 1, Pg
23 Th Functon cos sn Physcs 01: Lctur 1, Pg 3
24 Th Functon cos sn Physcs 01: Lctur 1, Pg 4
25 Th Functon cos sn Physcs 01: Lctur 1, Pg 5
26 Th Functon cos sn Physcs 01: Lctur 1, Pg 6
27 Th Functon cos sn Physcs 01: Lctur 1, Pg 7
28 Clckr Quston 4: What s th nnr product of ths two complx vctors <u w>? (a) 1 u 1 1 (b) 0 (c) 1/ (d) cos 0 t w t t () sn 0t Physcs 01: Lctur 1, Pg 8
29 / Clckr Quston 5: Dtrmn th valus of A and that xprss th complx numbr c = + n th form A A. B. C. D. / 4 / 4 / 4 E. Somthng ls Physcs 01: Lctur 1, Pg 9
30 Clckr Quston 6: Suppos z = 1-. What s z? A. B. cos C. 1 D. E. Somthng ls Physcs 01: Lctur 1, Pg 30
31 Exrcs 1 1 S cos Show that. cos Physcs 01: Lctur 1, Pg 31
Diffraction. Diffraction: general Fresnel vs. Fraunhofer diffraction Several coherent oscillators Single-slit diffraction. Phys 322 Lecture 28
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Diffraction. Diffraction: general Fresnel vs. Fraunhofer diffraction Several coherent oscillators Single-slit diffraction. Phys 322 Lecture 28
Chapt 10 Phys 3 Lctu 8 Dffacton Dffacton: gnal Fsnl vs. Faunhof dffacton Sval cohnt oscllatos Sngl-slt dffacton Dffacton Gmald, 1600s: dffacto, dvaton of lght fom lna popagaton Dffacton s a consqunc of
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