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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