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Physics .

section : J -n- hong Huang

-

Th 4 -I pm .

my OH : weds after lecture .

- or : send email anytime .

Wah : weekly HWsubmit viacanvas .

-

due Mondays.-

(Hwi due April 6 .) / Pdfstypesetting ,

• More-

i.e . many - body Q .M

.

-

Give Input !-

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1. An indefinite # of identical particles.- --

( " second quantization". )

aka "

quantum field theory

( in ratings;! ÷!" )1-I SHI .Vfx) = Vcxo) -10 + {V'

'

ar.> Cx-x.PWLOG Xo = 0 . +bH

anharmonicH -- Ian ttzmwx' terms .

- Q=fEx=tECP'to) t

= tout ata th )P ¥u P

Pr Laa=¥QtiP ) Iqat = (Q- IP )

. -

a

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Ex ,p7=ihH ⇒ [ a. at) - y

D= ata H'- taint's )

[ N , a ) - -a CN,at ) -_ at .

a. at are loamy &raTfnN .

N^lh7=nln ) . Flath>) - (att at In >

= @that In > .

o Illam>K' = Lnlataln> =LnlN1n>= n Lulu >

⇒ a=o .

I

107, 177

-- at 107

,.

. - In) -- chat )" to>

I -- Lulu)=DCn=f¥.

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I Particles .f&=andIKomal tomorrowMTx ,-- a Xena - - - Xkna kN tNtFX,

9rtI=9,H-omas¥qIEmk⑥

qu

u + EE.it/-iiI/hfEab8a9b-@-observation" T :{9,92 . . .gr#fsl9r9s---9N9,}

Pi - - - Pm Pw MPs - - Prv

is asymmetry . [ H , T) = o .-

[hk,-13=0 -

tf! ! ! !: :) hast . -- Tanks.*-

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T (x ) = Xt a .

Teihx = eihlxta)= eiha eihx

- In

slogans : linear & hand- innit

⇒ solvable by Fourier .

Nor#:Xn=anNf = eihxngn = E.HenkK - F{ I = faE.ae"" Pm nxn unitaryKT matrix .

auxiliary on problem :

H = span {In> , thxNS

= In >}u'

Tin -- int ' > Ti"rIghgFff- = €

,

I ht'll 4 8 03°

o

1h > = ⇐ eihnaln > sy

F Ik) = e "hanky .

nhwmutmeiprstate .

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Regulators : Nifnite ( IR)

q Ign.in#1=ehpNa ⇒ k,Jex .

→a s finite ( lattice I

only neigh? arene →h=oeinasadenth t{÷m,

→ Nvawe$k€##T#TI'um=t " :!÷÷z÷.I nnkuutn .

-- h . .

% um Uni ' " tbh ' 's

j ,= E Yen Uhf = NL ⇐ezlkttdna

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{pi = En En, Unh Pu Unh' Ph '

FI, E Lunin)tUnh Ph Ph 'u!. u)= thin

= Sii,k

= En Pup-u .

-

E (9n9nP=§¢T-e) IT§ En, (e-

ihha- 1) (e-

ihha- i) qq .

- Kha -Ahh-

→ Shih '

=§ 4 sin'

HE % fu .

-

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H -- { fPhf + Emwigeon )Y

Wn = zfEu sin 1k¥"

25¥ EH+6163)"

t±÷÷÷:÷istofu

-- 19in

,H) = Pna ittpn -- Cpn , H )

→ m gin = -K ( 29N - 9h-i- 9mi )-→ m Ijn = - K(2 - 2cos ha ) ga

tis -K2sin 16142 8h .

8h47 = { e-iwtgaw

}-

→ o = (w'-wi)gawk @2- Vik) quot. . .--

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Vs = IIh/↳o=afE .

Wahl← ( zf-via ) GAH = o .

eguIT -

.

x-onrtn.E.onno.mx#nrx*mIhoo--qnroInHomeYmy•n-oImxSoundwave . →

quantumsound wave

= phonon .who is qcx.tn ? -

÷÷÷"n"

- tox

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µ} wa-- sinha

classical .-hlong shirt

warilyh rawleyL