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

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    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.:

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    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

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    @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)

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    '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('

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    /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 =

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    !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%"

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    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 wa

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