7/24/2019 Particle Wave Duality 1
1/31
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
7/24/2019 Particle Wave Duality 1
2/31
Man ."=./
Alastair Rae Qan.m M"!1an!/ &IoP' &$2 ?? !%o/"/. .o !or/"'
Brehm and Mullin In.ro
7/24/2019 Particle Wave Duality 1
3/31
SYLLABUS
7/24/2019 Particle Wave Duality 1
4/31
SYLLABUS (cont)
7/24/2019 Particle Wave Duality 1
5/31
5
P1o.o?"%"!.r! "ff"!.: Com4.on
/!a.."rng
a//on?G"rm"r "=4"rm"n.:
7/24/2019 Particle Wave Duality 1
6/31
DAVE PARTICLE UALITY
Evidence for wave-particle dualityPhotoelectric effect
Compton effect
Electron diffraction
nterference of matter-wave!
Con!e"uence#$ei!en%er& uncertainty principle
7/24/2019 Particle Wave Duality 1
7/31
PHOTOELECTRIC EECT
'hen li&ht i! !hone on a metal plate in a vacuum, it emit!
char&ed particle! ($ert* 1++), which were later !hown to %eelectron! %y .. /hom!on (1+).
Electric field E of li&ht eert! force
F-eEon electron!. 3! inten!ity of
li&ht increa!e!, force increa!e!, !o 4E
of e5ected electron! !hould increa!e.
Electron! !hould %e emitted whatever
the fre"uency 6 of the li&ht, !o lon& a!
Ei! !ufficiently lar&e
7or very low inten!itie!, epect a time
la& %etween li&ht epo!ure and emi!!ion,
while electron! a%!or% enou&h ener&y to
e!cape from material
Classical expectations
Hertz J.J. Thomson
acuum
cham%er
8etalplate
Collectin&
plate
3mmeter
Potentio!tat
9i&ht, fre"uency 6
http://images.google.co.uk/imgres?imgurl=br.geocities.com/saladefisica3/fotos/hertz.gif&imgrefurl=http://br.geocities.com/saladefisica3/&h=302&w=223&prev=/images%3Fq%3Dhertz%26svnum%3D10%26hl%3Den%26lr%3D%26ie%3DUTF-8%26oe%3DUTF-8%26sa%3DG7/24/2019 Particle Wave Duality 1
8/31
PHOTOELECTRIC EECT &!on.'
/he maimum 4E of an emitted electron i! then
maK h W=
Work function# minimum
ener&y needed for electron to
e!cape from metal (depend! on
material, %ut u!ually 2-:e)
Planck constant#
univer!al con!tant of
nature
;et!
of ener&y (photons)
3n electron a%!or%! a
!in&le photon to leave
the material
7/24/2019 Particle Wave Duality 1
9/31
Photoemi!!ion eperiment! today
8odern !ucce!!or to ori&inal photoelectric
effect eperiment! i!ARPES (Angle-
Resole!PhotoemissionSpectroscop"#
Emitted electron! &ive information on
di!tri%ution of electron! within a material
a! a function of ener&y an!momentum
7e%ruary 2000
7/24/2019 Particle Wave Duality 1
10/31
@883AB 7 P$/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.'
7/24/2019 Particle Wave Duality 1
15/31
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)
7/24/2019 Particle Wave Duality 1
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
7/24/2019 Particle Wave Duality 1
17/31
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*
= =
7/24/2019 Particle Wave Duality 1
18/31
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('
7/24/2019 Particle Wave Duality 1
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 =
7/24/2019 Particle Wave Duality 1
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
7/24/2019 Particle Wave Duality 1
21/31
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.
7/24/2019 Particle Wave Duality 1
29/31
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%"
7/24/2019 Particle Wave Duality 1
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
7/24/2019 Particle Wave Duality 1
31/31
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