Phy

sics

2D

Lec

ture

Slid

esN

ov 4

Viv

ek S

harm

aU

CSD

Phy

sics

Boh

r’s E

xpla

natio

n of

Hyd

roge

n lik

e at

oms

•B

ohr’

s Sem

icla

ssic

alth

eory

exp

lain

ed so

me

spec

trosc

opic

da

ta

Nob

el P

rize

: 192

2•

The

“hot

ch-p

otch

” of

cla

sica

l& q

uant

um a

ttrib

utes

left

man

y (E

inst

ein)

unc

onvi

nced

–“a

ppea

red

to m

e to

be

a m

iracl

e –

and

appe

ars

to m

e to

be

a m

iracl

e to

day

......

One

oug

ht to

be

asha

med

of t

he s

ucce

sses

of t

he th

eory

”

•Pr

oble

ms w

ith B

ohr’

s the

ory:

–Fa

iled

to p

redi

ct IN

TEN

SIT

Y o

f spe

ctra

l lin

es

–Li

mite

d su

cces

s in

pre

dict

ing

spec

tra o

f Mul

ti-el

ectro

n at

oms

(He)

–Fa

iled

to p

rovi

de “

time

evol

utio

n ” o

f sys

tem

from

som

e in

itial

stat

e–

Ove

rem

phas

ized

Par

ticle

nat

ure

of m

atte

r-cou

ld n

ot e

xpla

in th

e w

ave-

parti

cle

dual

ity o

f lig

ht

–N

o ge

nera

l sch

eme

appl

icab

le to

non

-per

iodi

c m

otio

n in

sub

atom

ic

syst

ems

•“C

onde

mne

d” a

s a o

ne tr

ick

pony

! W

ithou

t fun

dam

enta

l in

sigh

t …ra

ised

the

ques

tion

: Why

was

Boh

r suc

cess

ful?

Ato

mic

Exc

itatio

n by

Ele

ctro

ns: F

ranc

k-H

ertz

Exp

tO

ther

way

s of E

nerg

y ex

chan

ge a

re a

lso

quan

tized

! Ex

ampl

e:

•Tr

ansf

er e

nerg

y to

ato

m b

y co

llidi

ng e

lect

rons

on

it•

Acc

eler

ate

elec

trons

, col

lide

with

Hg

atom

s, m

easu

re e

nerg

y tra

nsfe

r in

inel

astic

col

lisio

n (r

etar

ding

vol

tage

)

Ato

mic

Exc

itatio

n by

Ele

ctro

ns: F

ranc

k-H

ertz

Exp

tPl

ot #

of e

lect

rons

/tim

e (c

urre

nt) o

verc

omin

g th

e re

tard

ing

pote

ntia

l (V

)

Equa

lly sp

aced

Max

ima

and

min

ima

in I-

V c

urve

Ato

ms a

ccep

t onl

y di

scre

te a

mou

nt o

f Ene

rgy,

no

mat

ter t

he fa

shio

n in

whi

ch e

nerg

y is

tran

sffe

red

∆E

∆E

Prin

ce L

ouis

e de

Bro

glie

•K

ey to

Boh

r ato

m w

as A

ngul

ar m

omen

tum

qua

ntiz

atio

n•

Why

Qua

ntiz

atio

n m

vr=

|L|

= nh

/2π

?•

Invo

king

sym

met

ry in

nat

ure

the

Prin

ce d

eBro

glie

post

ulat

ed

–B

ecau

se p

hoto

ns h

ave

wav

e an

d pa

rtic

le li

ke n

atur

e pa

rtic

les

mus

t hav

e w

ave

like

prop

ertie

s –

Elec

tron

s ha

ve a

ccom

pany

ing

“pilo

t” w

ave

(not

EM

) whi

ch g

uide

pa

rtic

les

thru

spa

cetim

e.

•M

atte

r Wav

e :

–“P

ilot w

ave”

of

Wav

elen

gth λ=

h /

p =

h / (γm

v)–

freq

uenc

y

f = E

/ h

•If

mat

ter

has w

ave

like

prop

ertie

s the

n th

ere

wou

ld b

e in

terf

eren

ce (d

estr

uctiv

e &

con

stru

ctiv

e)•

Use

ana

logy

of s

tand

ing

wav

es o

n a

pluc

ked

stri

ng to

ex

plai

n th

e qu

antiz

atio

n co

nditi

on o

f Boh

r or

bits

Mat

ter W

aves

: H

ow b

ig, h

ow s

mal

l

3434

1.W

avel

engt

h of

bas

ebal

l, m

=140

g, v

=27m

/sh

6.63

10.

=

p(.1

4)(

27/

)

size

of n

ucle

us

Bas

ebal

l "lo

oks"

2. W

avel

engt

h of

ele

ctr

like

a pa

rticl

e

1.75

10

baseball

hJs

mv

kgms

m

λ

λ−

−×

=

<<<

=

⇒

×=

⇒

1

2

-31

19

-24

3

20

4

4

on K

=120

eV (a

ssum

e N

R)

pK

=2

2m

=

2(9.

1110

)(120

)(1.6

10)

=5.

91 1

0.

/6.

6310 Siz

e

.5.

9110

./

of

at

1

o

1.12

0e

e

pmK

eV

Kgms

Js

kgms

hm

p

λ

λ

−

−

−−

⇒=

××

×

×=

=×

⇒

=×

m !!

Mod

els

of V

ibra

tions

on

a Lo

op: M

odel

of e

in a

tom

Mod

es o

f vib

ratio

n w

hen

a in

tegr

al

# of

λfit

into

lo

op( S

tand

ing

wav

es)

vibr

atio

ns c

ontin

ue

Inde

finite

ly

Frac

tiona

l # o

f wav

es in

a

loop

can

not

per

sist

due

to

dest

ruct

ive

inte

rfer

ence

De

Bro

glie

’sE

xpla

natio

n of

Boh

r’s Q

uant

izat

ion

Stan

ding

wav

es in

H a

tom

:

sCon

stru

ctiv

e in

terf

eren

ce w

hen

n =

2r

Ang

ular

mom

entu

m

Qua

ntiz

atio

n co

ndit

ince

h=

p

....

..

io!

()

2

n

h mNR

nhr

m nmvr

v

v

λπ λ

π⇒ ⇒

=

==n

= 3

This

is to

o in

tens

e ! M

ust v

erify

such

“lo

ony

tune

s” w

ith e

xper

imen

t

Rem

inde

r: Li

ght a

s a

Wav

e : B

ragg

Sca

tterin

g E

xpt

Inte

rfer

ence

Pa

th d

iff=2

dsinϑ

= nλ

Ran

ge o

f X-r

ay w

avel

engt

hs sc

atte

rO

ff a

cry

stal

sam

ple

X-r

ays c

onst

ruct

ivel

y in

terf

ere

from

C

erta

in p

lane

s pro

duci

ng b

right

spot

Ver

ifica

tion

of M

atte

r Wav

es: D

avis

son

& G

erm

erE

xpt

If e

lect

rons

hav

e as

soci

ated

wav

e lik

e pr

oper

ties

expe

ct in

terf

eren

ce

patte

rn w

hen

inci

dent

on

a la

yer o

f ato

ms (

refle

ctio

n di

ffra

ctio

n gr

atin

g) w

ith in

ter-

atom

ic se

para

tion

d su

ch th

at

path

diff

AB

= ds

inϑ

= nλ

Laye

r of N

icke

l ato

ms

Ato

mic

latti

ce a

s diff

ract

ion

grat

ing

Ele

ctro

ns D

iffra

ct in

Cry

stal

, jus

t lik

e X

-ray

s

Diff

ract

ion

patte

rn

prod

uced

by

600

eVel

ectro

ns in

cide

nt o

n a

Al f

oil t

arge

t

Not

ice

the

wax

ing

and

wan

ing

of

scat

tere

d e

lect

ron

Inte

nsity

.

Wha

t to

expe

ct if

el

ectro

n ha

d no

wav

e lik

e at

tribu

te

Dav

isso

n-G

erm

erE

xper

imen

t: 54

eV

elec

tron

Bea

m

Scattered Intensity

Pola

r Plo

tC

arte

sian

plo

t

max

Max

scat

ter a

ngle

Pola

r gra

phs o

f DG

exp

twith

diff

eren

t ele

ctro

n ac

cele

ratin

g po

tent

ial

whe

n in

cide

nt o

n sa

me

crys

tal (

d =

cons

t)

Peak

at Φ

=50o

whe

n V

acc

= 54

V

Ana

lyzi

ng D

avis

son-

Ger

mer

Exp

twith

de

Bro

glie

idea

10ac

c

acc

22

de B

rogl

ie

for e

lect

ron

acce

lera

ted

thru

V=5

4V

12

; 2

2If

you

belie

ve d

e B

rogl

ie

h=

2

(de

Br

2

V =

54

Vol

ts1.

6og

p2

Flie

)Ex

ptal

d7

10

or

predict

peV

mv

KeV

vm

m

hh

mv

eVm

m

eVpmvm

m

h meV

m

λ

λλ

λ−

•=

==

⇒=

==

=

=

×

=

=

⇒=

nick

elm

-10

ax

ata

from

Dav

isso

n-G

erm

er O

bser

vatio

n:

Diff

ract

ion

Rul

e : d

sin

=

=2.1

510

(fro

m B

ragg

Sca

tterin

g)

(obs

erva

tion

from

scat

terin

g in

tens

ity p

n

d=2

.15

A

50lo

o

)

F

t

rP

odiff

m

θ

φλ

=

⇒

×

pred

oic

t

obse

rv

1.67

rinci

pal M

axim

a (n

=1);

=

agr

eem

ent

(2.1

5 A

)(si

n =

150

).6

5 meas

AExcellent

Aλ

λλ

=

Dav

isso

nG

erm

erE

xper

imen

t: M

atte

r Wav

es !

Exce

llent

Agr

eem

e2

nt

predict

h meV

λ=

Pra

ctic

al A

pplic

atio

n : E

lect

ron

Mic

rosc

ope

Elec

tron

Mic

rogr

aph

Show

ing

Bac

terio

phag

eV

iruse

s in

E. C

oli b

acte

rium

The

bact

eriu

m is

≅1µ

size

Ele

ctro

n M

icro

scop

e : E

xcel

lent

Res

olvi

ng P

ower

Wes

t Nile

Viru

s ex

tract

ed fr

om a

cro

w b

rain

Just

WH

AT

is W

avin

g in

Mat

ter W

aves

?•

For w

aves

in a

n oc

ean,

it’s

the

wat

er th

at “

wav

es”

•Fo

r sou

nd w

aves

, it’s

the

mol

ecul

es in

med

ium

•

For l

ight

it’s

the

E&

Bve

ctor

s •

Wha

t’s w

avin

g fo

r mat

ter

wav

es ?

–It’

s th

e PR

OB

AB

LILI

TY O

F FI

ND

ING

TH

E PA

RTI

CLE

that

w

aves

!–

Part

icle

can

be

repr

esen

ted

by

a w

ave

pack

et in

•

Spac

e •

Tim

e •

Mad

e by

supe

rpos

ition

of

man

y si

nuso

idal

wav

es o

f di

ffer

ent λ

•It

’s a

“pu

lse”

of p

roba

bilit

y

Imag

ine

Wav

e pu

lse

mov

ing

alon

g a

strin

g: it

s loc

aliz

ed in

tim

e an

d sp

ace

(unl

ike

a pu

re h

arm

onic

wav

e)

Wav

e pa

cket

repr

esen

ts p

artic

le p

rob

loca

lized

Mak

ing

Wav

e pa

cket

s w

ith S

inus

oida

l Wav

es: M

odel

11

12

12

12

ff

f-f

Wa

Ex:

Phe

nom

enon

of "

Bea

ting"

A

dd tw

o w

aves

of s

light

ly d

iffer

ent

, f

Star

t with

two

wav

es

y(

),

in S

ve w

ith :

f =

, Am

p

ound

litud

e A

2

:

y

2

ACoskxwt

ACos

λ+

⎛⎞

⎛⎞

⇒∝

⎜⎟

⎜⎟

⎝

=−

=

⎠⎝

⎠

22

2(

):,

2kxwtk

wf

ππ

λ−

==