particle wave duality 1

7/24/2019 Particle Wave Duality 1

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QUANTUM THEORY PHYS2B22

EVENING CLASS 2005

Lecturer Sam Morgan Off!"# A$2

T"%# &020' ()(* +,-) &In."rna%# ++,-)'

Ema%# /am.1"or341/3!%3a!36

Website 1..4#778883.am4a341/3!%3a!3679/am72B2231.m%

Con.an/# L"!.r" no."/: 4ro;%"m /"./ an< 4a/. "=am 4a4"r/

Assessment: *0> on /mm"r "=am$0> on ;"/. + of , 4ro;%"m /1""./

NB r%"/ on "=am 8.1


2/31

Man ."=./

Alastair Rae Qan.m M"!1an!/ &IoP' &$2 ?? !%o/"/. .o !or/"'

Brehm and Mullin In.ro


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SYLLABUS


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SYLLABUS (cont)


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5

P1o.o?"%"!.r! "ff"!.: Com4.on

/!a.."rng

a//on?G"rm"r "=4"rm"n.:


6/31

DAVE PARTICLE UALITY

Evidence for wave-particle dualityPhotoelectric effect

Compton effect

Electron diffraction

nterference of matter-wave!

Con!e"uence#$ei!en%er& uncertainty principle


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PHOTOELECTRIC EECT

'hen li&ht i! !hone on a metal plate in a vacuum, it emit!

char&ed particle! ($ert* 1++), which were later !hown to %eelectron! %y .. /hom!on (1+).

Electric field E of li&ht eert! force

F-eEon electron!. 3! inten!ity of

li&ht increa!e!, force increa!e!, !o 4E

of e5ected electron! !hould increa!e.

Electron! !hould %e emitted whatever

the fre"uency 6 of the li&ht, !o lon& a!

Ei! !ufficiently lar&e

7or very low inten!itie!, epect a time

la& %etween li&ht epo!ure and emi!!ion,

while electron! a%!or% enou&h ener&y to

e!cape from material

Classical expectations

Hertz J.J. Thomson

acuum

cham%er

8etalplate

Collectin&

plate

3mmeter

Potentio!tat

9i&ht, fre"uency 6
http://images.google.co.uk/imgres?imgurl=br.geocities.com/saladefisica3/fotos/hertz.gif&imgrefurl=http://br.geocities.com/saladefisica3/&h=302&w=223&prev=/images%3Fq%3Dhertz%26svnum%3D10%26hl%3Den%26lr%3D%26ie%3DUTF-8%26oe%3DUTF-8%26sa%3DG


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PHOTOELECTRIC EECT &!on.'

/he maimum 4E of an emitted electron i! then

maK h W=

Work function# minimum

ener&y needed for electron to

e!cape from metal (depend! on

material, %ut u!ually 2-:e)

Planck constant#

univer!al con!tant of

nature

;et!

of ener&y (photons)

3n electron a%!or%! a

!in&le photon to leave

the material


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Photoemi!!ion eperiment! today

8odern !ucce!!or to ori&inal photoelectric

effect eperiment! i!ARPES (Angle-

Resole!PhotoemissionSpectroscop"#

Emitted electron! &ive information on

di!tri%ution of electron! within a material

a! a function of ener&y an!momentum

7e%ruary 2000


10/31

@883AB 7 P$/D PAPEA/E@@883AB 7 P$/D PAPEA/E@

E h=

h hp c

= =

E =h

p k=h

2

h

=h

2

k

=

Ener&y and fre"uency

3l!o have relation %etween momentum and wavelen&th

2 2 2 2 .

/hi! come! from a colli!ion %etweenthe -ray photon and the nucleu! of

the atom

( )1 co! 0(

h

m c = :

( em m?!ince!ince

COMPTON SCATTERING

&!on.'


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DAVE?PARTICLE UALITY O LIGHT

In 1924 Einstein wrote:- There are therefore now two

theories of light, both indispensable, and without anylogial onnetion!"

Evidence for wave-nature of li&htGiffraction and interference

Evidence for particle-nature of li&htPhotoelectric effectCompton effect

9i&ht ehi%it! diffraction and interference phenomena thatare onl"eplica%le in term! of wave propertie!

9i&ht i! alway! detected a! pac>et! (photon!)K if we loo>,

we never o%!erve half a photon

Dum%er of photon! proportional to ener&y den!ity (i.e. to

!"uare of electroma&netic field !tren&th)


16/31

'e have !een that li&ht come! in di!crete unit! (photon!) withparticle propertie! (ener&y and momentum) that are related to the

wave-li>e propertie! of fre"uency and wavelen&th.

MATTER DAVES

h

p=

n 12; Prince 9oui! de Lro&lie po!tulated that ordinary matter can have

wave-li>e propertie!, with the wavelen&th)related to momentumpin the !ame way a! for li&ht

de Lro&lie wavelen&th

de Lro&lie relation

;M! con!tant

.re,iction:'e !hould !ee diffraction and interference of matter wave!

De Broglie

DL wavelen&th depend! on momentum, not on the phy!ical !i*e of the particle


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E!timate !ome de Lro&lie wavelen&th!

'avelen&th of electron with :0e >inetic ener&y

2 210

21. 10 m

2 2 2e e e

p h hK

m m m K

= = = =

'avelen&th of Ditro&en molecule at room temperature

u

11

;, 8a!! 2+m

2

2.+ 10 m;

k*K

h

+k*

= =

= =

'avelen&th of Au%idium(+) atom at :0n4

=1.2 10 m

;

h

+k*

= =


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Davisson .P. Thomson

Gavi!!on, C. .,

N3re Electron!

'ave!O,N 7ran>linn!titute ournal

%"#, : (12+)

/he Gavi!!on-ermer eperiment#!catterin& a %eam of electron! from

a Di cry!tal. Gavi!!on &ot the 1;

Do%el pri*e.

3t fied acceleratin& volta&e (fied

electron ener&y) find a pattern of !harpreflected %eam! from the cry!tal

3t fied angle, find !harp pea>! in

inten!ity a! a function of electron ener&y

.P. /hom!on performed !imilar interference

eperiment! with thin-film !ample!

Fi

Fi

ELECTRON IRACTIONELECTRON IRACTION

T1" a//on?G"rm"r "=4"rm"n. &$*2('T1" a//on?G"rm"r "=4"rm"n. &$*2('


19/31

/nterpretation:!imilar to Lra&& !catterin& of -ray! from cry!tal!

a

Fi

Fr

co!i

a

co! ra

.at' ,i++erence:

Constructi*e inter+erence 'en

Dote difference from u!ual HLra&&M! 9awI

&eometry# the identical !catterin& plane! are

orientedperpen!icularto the !urfaceDote $iand$rnot

nece!!arily e"ual

Electron !catterin&

dominated %ysurface

layer!

ELECTRON IRACTION &!on.'ELECTRON IRACTION &!on.'

(co! co! )r ia

(co! co! )r ia n =


20/31

!in!

ri&inally performed %y Boun& (1+01) to demon!trate the wave-nature of li&ht.

$a! now %een done with electron!, neutron!, $e atom! amon& other!.

,

F!

Getectin&

!creen

ncomin& coherent%eam of particle!

(or li&ht)

"

3lternative

method ofdetection# !can a

detector acro!!

the plane and

record num%er of

arrival! at each

point

THE OUBLE?SLIT EPERIMENT

7or particle! we epect two pea>!, for wave! an interference pattern


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Deutron!, 3 Qeilin&er

et al% 1++Reie's of

+o!ern Ph"sics 0"10=-10;

$e atom!# Carnal and 8lyne>

11Ph"sical Reie' Letters 00

2=+-2=2

C=0molecule!# 8

3rndt et al% 1

ature 1" =+0-

=+2'ith

multiple-!lit

&ratin&

'ithout &ratin&

EPERIMENTAL RESULTS

nterference pattern! can not %e eplained cla!!ically - clear demon!tration of matter wave!

7rin&e

vi!i%ility

decrea!e! a!

molecule! areheated. 9.

$ac>ermRller

et al%200 of determini!m) i! intrin!ic to the theory.


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HEISENBERG UNCERTAINTY PRINCIPLE

D" 8%% /1o8 forma%% &/"!.on ,'

J 2

J 2

J 2

3

"

z

3 p

" p

z p

h

h

h

D" !anno. 1a" /m%.an"o/ 6no8%"


30/31

T1"r" / a%/o an "n"rg?.m" n!"r.an. r"%a.on

Tran/.on/ ;".8""n "n"rg %""%/ of a.om/ ar" no. 4"rf"!.%

/1ar4 n fr"F"n!3

J 2E t

h

n +

n 2

n $

;2E h=

;2

In."n

/.2

r"F"n!

;2

HEISENBERG UNCERTAINTY PRINCIPLE

T1"r" / a !orr"/4on


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CONCLUSIONS

9i&ht and matter ehi%it9i&ht and matter ehi%it wave-particle dualitywave-particle duality

Aelation %etween wave and particle propertie!Aelation %etween wave and particle propertie!

&iven %y the&iven %y the de Lro&lie relation!de Lro&lie relation!

Evidence for particle propertie! of li&htEvidence for particle propertie! of li&htPhotoelectric effect, Compton !catterin&Photoelectric effect, Compton !catterin&

Evidence for wave propertie! of matterEvidence for wave propertie! of matter

Electron diffraction, interference of matter wave!Electron diffraction, interference of matter wave!(electron!, neutron!, $e atom!, C=0 molecule!)(electron!, neutron!, $e atom!, C=0 molecule!)

$ei!en%er& uncertainty principle$ei!en%er& uncertainty principlelimit!limit!

!imultaneou! >nowled&e of con5u&ate varia%le!!imultaneou! >nowled&e of con5u&ate varia%le!

hE h p

= =

:

J 2

J 2

J 2

3

"

z

3 p

" p

z p

h

h

h

particle wave duality 1

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