1. e0 cmo nuc vADAoTAo
DAI HOCUUP
Hq ud,t€n thi s'inh:.
56 bd,odanh:
KY THI TUYEN SINH SAU DAI HoC xAvT 2006
M6n thi: Vdt li Ly thuyct
lrtctng
hat vi
D),nh cho:Cao hoc
Thdi gian lb,mbd,i:180phirt
A. CO HQC LUQNG TU
Cdu 1: Dao hdm cfia to5,ntfi theo thdi gian vb,tich phAn chuydndOngtrong co hoc
ttt. Chfing minh rang n5,ngluong E vb,hinh chi€tip, ctraxung luong tr€n truc Or cta
mOchuyOndOngtu do lb,nhfrng tich phAn chuydndOng.
CAu 2: TronghCtoa dOcau (r,0,@),toan trl hinh chi€umOmenxung h-tongco dang:
^ a l
L,:-ih^,v6t0<0<.2n.-d6
1. Tim tri ri€ng va ham ri€ng chud,nho5,cria to5,ntfr L".
2. Tim x5,csu6t do dudc c5,ctri ri€ngL, khi hat 6 trang thai ,!@) -
trring binh cfi,aL" 6 trang tliSi ndy.
cos@va tri
B VAT IY THONG KE
CAu 3: Th6ng ke luong trl cirah€ hat bosondOngnh6t : ThOngk€ Bose-Einstein,
CAu 4: Cho mQthe khi ly tLr6ng.
a) Til phdn b6 chinh tdc Gibbs, hay suy ra ph6,nb6 Ma-xwell-BoltzmanndOiv6i h€
dilt trong trudng lr,rc.
b) Viet bi€ii thirc cr'ias6 phAn tir kiri ly tudng c6 dOl6n vAn t6c ndm trong khoing
lr,,,uI dul, trong do du Ia luong bi€n thiOnvi c6p cfradOldn vdn t6c u.
c) Tim gi6 tri trung binh, gia tri tod,nphudngtrnng binh, gi6 tri c6 x6.csr-rAtcuc dai
ciia vAnt6c klii ly tudng.
Cho bi€t cactich ph6n (vdi a > 0):
1,35...(2,- 1)
/,*
) n - ^ - 2 ,
,r"," p g&
d/r -
v w & -
2n+t
nt
2A"+1'
n: I,2,3,...
n - 0,I,2,...
Ghi chti";Thi sinh khOngduqc st dung td,ili€u. Cd"nb0 coi thi kh7ng gidi thich gi
th,€m.
/r*
,2n*7 e-o" d"r -
7(
Arrt+1

2. B0 GIAO DUC VA DAO TAO Hp vdftn thfsinh:
EAI HOCI{t'E SAbaodanh:
l' -- ';
e '
Ki' THI TUYENSINHSAUDAI HQCNAM 2OO7
-J€- (:'-oC
MOnthi:V$tly r! thuy6t
(ddnhcho Caohpc)
Thbi granldmbai: 180phrit
CAUI
Hdm songd thbi di6mdductramOthatco ktrdilugngm chuy0ndOngt'udo
frongmi6n 0<x<a c'ianOtn6w6ng g6c,1chiOu,s6uvOhan,c6dang:
v(x,o)=^E [,*ro,[=)l ri"[e)Y)4 1 a/) a)
1. X6cdinhhdms6ngV(x,t) twthbridi0mt >o Uatlcy.
2. Tinhnangluwg trungbinh0 thdi diOmdAuvdthdi diOmI >0.
3. X6cdinhxdcsu6ttimthAyhatdnuaf6ictanOtn6(mi6n0<r <alz)tarthdi
di6mr>o.
CAUII
Trangth6i co bdn criadiQntu tong nguy€ntu Hydro dugcm6 ta boi hdm
. (r)t" ( r
s6ng4o =zl- | expl-- l, trongc16a ld bankinh quyclaoBohr thr?nhat.Hdy xitc
a) a) .
dinhbdnkinh r rmgvdi x5csu6ttim th6ydiOntu cuc dai.
CduIII
X6c clinhphucrngbinh trangthdi cta hekhi l)?tucmgdm nguy€ntu g6mN
nguy6ntu khi; bi6tring, ndngluqmgvd xungluqng criac6cphdntti khi li6n h0vdi
nhaubdi hethric1t =cp(c: const).
+co
ChobiOtf (a)=
t *"-"-*dx, l(n +1): nl,
0
CduIV
Kh6osit hON hatkh6ngtucrngt6cmi ndngluqrg criam6i hatkhi o ffongtu
ffumg coth6nhanmQttrongba gpdtri 0, e t pll . Xdcdinh nanglucr,ngE vd friet
dungCvcuahQ.
CAUV,
1. Tim x6csuAtcriachcgi6tr1L, L<fiihatd tronghangth6idugcmdti boi hdm
s6ngfrongtqad0cAu:V(D= ^E sur|,vfi 0<O32n .
77
2. Tim ndnglucmgtrungbinh vd nhiOtdungcuah0 .^/hat kh6ngtuongtitc, biet
rangnn6ihatcotheOfronghaitangthdi luqngtu kh6ngsuybi6nvdi c6cgletr|
ndngluqngld eovd e,.
Ghichrt:Cdnb0coithikh1nggidi thfchgi th€m.

3. e0 cilo DUCvA DAorAo/
D4r HOC HUE
Hg ud"t€n th( s'inh:
56 bd,odanh:
KV THI TUYfiN SINH SAU DAI Hoc NAvt 2008
MOnthi: vAr n* n* THUY6T
(d,d,nhcho Cao hPr)
Thdi gian ld'm bd'i':180 Phft
cau I. Tlang thSi cria m6t hat duoc m6 ta bxng hdm s6ng
t 2 | : l ^ -
,b@)- Ae-iP''*' ,
trong d6 A, a vd,k ld nhung hXng sd.
a. X6c dinh thira sd chudn h6a A. T)m toa d6 r dd cho mat do sudttim thdy hat p(r) co
gi6 tri i6n nhdt.
b. H5.ytinh c6cgi6 tri trung binh EP,M". Nghiamlai h6 thric b6t dinh giiia toa cl6vA,xung
Iuong.
Cho c6c c6ng thirc tich PhAn
hba mot chiEukhong
xac
l-:
e-o"'d,r-
sau:
f +co
I re-o" dr - 0,
J - x l_:
,2
"-ar2
d,r-
pdtr _ r,--- - n J r
.
2)pn 2
trong d6 B U trxng sd Boltrmann, T li nhi6t d6 tuy6t d6i cta h6, hhm ndng luong 11crlah6 c6
tinh chdt H ---+*oo khi xung luong suy r6ngpr -. 1e6.
Sri dung dinh t1iphdn b6 dbu d6ng n5,ngtheo ciic bA,ctr.rdo n6i tr6n vir dinh lf virian, tim
n5,ngluong lru"g bi"h crla dao d6ngtt tlibu hbatuy6n tinh cd didn'
CAu IV.
o. Ldp luAn dd d6n ra phAn b6 chinh t{c luong tt. DiEuki6n chudn h6a, tdng trang th6i vd
n5,nglucrngtu do trong phAnb6 chinh t6c luong.trl.
a. 1'tt lnan U?
"fri"it
td," lrrorrg1rl, hey thi6t I6p bidu thfrc th6ng ke Maxwell-Boltzmannluong
ti.
1
t
Cdu II. Dua tr6n toSntt toa d6 vi to6n tri il6ng lucrng,crich€ thfc giaoho6ngiila crlctor'n tti
toa d6 vd to6n ti dQngluong, h6y n6u dinh nghia vd vi6t bidu thric cria to6n tri m6mencl6ng
luong qui dao vi cd,chinh chi6ucria n6 trong hOtga dQDescartes''
bO tftAdo cluocchinh xric dbngthdi hai hinh chi6ucriam6mend6ngluong qui claotr6n ciic
phucrngkhiic nhau hay kh6ng? Chring minh.
cau III. Dtng phdn b6 chinh tdc Gibbs, chringminh dinh lf phan b6 dEu cl6ngndngtheo c5c
bAc tu do c6 dang
CAu V. Tlong co hoc lucyngtri, phd nd,nglucrngcria m6t dao d6ng tr} 'dibu
bi suy bi6n vh,c6 d+ttg
/ 1
€n:a("*r),
trong d,on - 0, 1,2,3,.. . ) u)Ih,tbn s6 dao dQttg.HAy tfnh n5ng lucrngtu do
dao d6rrgtu dibu hba mdt chiEud6c lAp, dao d6ng vdi cilng mQt thn s6'
b0
7r
o .
(lr
Ghi cht'r: Cd,n coi thi khong gid"i,thtch gi,th€m.
vd entropy cria he l/

4. BOGrAODUCVA DAOTAOt
DAI IIQC IIUE
Hq vd t2n thf sinh:..
SOOaodanh:
KV rHI ruynN sINHsAUDArHgc NAMz00e(DqtI)
Mdn thi: VAtIy Iy thuy6t
@dnhchocaohqc)
Thd'igtanldmbdi; 180 phrit
Ciu I. Hdm songo thoi di6m d0ucuamQthpt co khoi lugng m chuylndQngt.udo
tronggi€ngtfr6vuOnggoc,mQtchidu,bOrQnge, codang:
C ld hlne sOthuc.
1. Tim h0 s0chuAnhoaC.
2. X6c dinh chc gia fri ndng luq,ngdo duo.c vd x6c s.rAtcria c6c gi6 tr1ndy
trong trAngth6i tr6n. Tinh ndngluCmgtrung binh.
3. Xhc dinh hdm song v(x,t) tai thoi di€m r > 0 vh x6c s,t6td6 hat nim o
E ( sor -+ . ..2
trangthei g,r) = ^ll sinl:r:: ls h o thdi di€m r > 0.
Ya o )
Cdu II. Chimg minh rdngto6ntu hinh chi6um6mendQnglu-cmgtheophucrngtr.uc
zld,i,vd binh phuomgcuato6ntu ndy la c6ctoantu Hermite.
C6u III. Khdo s6the N hat kh6ng tucrng titc d trong thd tich V. Bi6t rlng d$ng
nlng cira phAntft khi li6n h€ voi xung lugng cua no theo h0 thuc € : a.p (a lir
hing sd).Hdy tinh tich phtn trang thili cuahQ,tu d6 x6c dinh m6i 1i6nh€ gifrangi
nf,ngU, frpsu6tP va th6tish V ciahE.
Ciu IV. BiCtring mQthat co spin * *t o trong tu trubng H, c6cmuc ndnglugng
L
ctran6 sCbt tfrchthenhhai muc - pH vd +FH tucrngung vdi c6cm6mentu -p vd
+p song song vd tl6i song vdi tu trucrng.Kh6o s6th€ N hat nhu th6 d trong tu
trucrngH vdi friet d0 T XAc dinh nQinlng U, entropyS vi nhiQtdungdangtich
Cv cuah0.
C0u V. Chrmg minh rdng ph6 ndng lucrngcua 1 dao clQngdi€u hod tuy6n tinh
luo.ngtu bang En=@+r'l2)tta. Su dungk6t qui trOndCtinh ndngluemgfrung
binh va nhi€t dung cuah€ ,^/ daocl0ngtu di6uhodtuy€ntinh luCmgtu dOc16pdao
dQngvoi cringtAns6 r .