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Quontum Mechoniss 1: 5250 o
Finel Exam Solns
Harmonic asc lletor
2
; = i Qe
AE LAO: eee
H = Bee al a2
f 2m Zz
“Bree por Heke in y,2
along, x 6
—%Bx 2 ikyrki
I Seg ie sioate N Hate e
} Where NY 1S ee a
Ko =e 5
- =P | hn
Using \ dx Hy (x) H(x)e Se n! Shams
[
ON: oy
=
| \% awe
| tr 4 2x,
r 2)j= oe =
Hl Mos ote) <a &L)*© |
vp
(b) Uz (x) = gE x 5 ha. eo
> f= ee si Pa rw x*- gEx
bal ie i = a € 2 2n2
H= Poy Be tw*(x ao
WY Car
=e =.
Sith ayeenitle: ado
Crea poche alloas y,% =
dirplacad iat i ose lladne with
. ~Ee. 2
<0} — Kao ihyy +ibe2
Zero of &n
2X
> Wea, &y2)= N Halse "e
Heirk’) e
Zr 2
t>0
En ky ky = Rw (n+45)+
UaRns olave Le eden p os) Hom MA Pe
| Sew = y™ ~%
ig _ Oye Sk,o | a
i %Or 2” xri2'n Zin € ar
8 | — &-a)* -
Jak Halete 7 Halse ™
oad Wins en Perbcmall Hy a Fig” S we yt:
A | dk,,0 Oks > Deel al eo “44
“ll iran nt mea
4%,
All = db, 0 Oka,0 1)” A 2
| 2g” Inv
if + an —h4
? te = One Oi Ont e
adro 4 cohuent ghd: -J2'2 =
= ~z
e 7 [n>
a ; _ &X%
A. - 2 e a
2 Y2 Jar’
©) wes) = ° G40
YF, oe) = = Cu" ot” e ees
2" ve int LEt epee
Qe (F 4) = Grool*®o) @
—~cwet
viaje) = Z So ~ (e ‘e. Pale kei
Ye Ini
-
nN
eS ee f ore mw) t
Ws
ta Zee" 6 8G ve soe
e =r © “ ar H, (x-«) @
Paaxils 8),
bee oe
&
yl) tty eualiegglle, ual es
| z v
| UwW)=-V, | Ske+a)+ Ta)
| Nx
OG) =O. except oA x= ta SU=2
| Grand stele is abound siete since
| in 1)~p Cy otbra chive potential = locvend Soak
(> = -°
+KX
i > Wes is) |) Preor com biacAina of @
|
xeta h d* ae =» = Pere
lea ae? = EP Pre
1 Pew hy oyeenedin UP, Hi =e > Lryprvletey
oes oan een under parity. Gs. 1S
| nae even (Symmelcie) “sing east # of
13 enough to jrot Jook at Y (x) tee x>oO
| We 6) = ACOSL RX | oxx<e@
| ~ RX
€ : a<x
|
|
|
| Acwoshkx, -9ex<0
ee _
Xk)=Xe a STxAi] QO)
el Ueex4)= | Bx e
‘ X(j)=Ke
S = (bm x7
Ke x (M+ TX (4)
K te) = ee OXK') x0
(o<t'2€ + 8X(e)=OxXA)=0
KK) = Xe=Ke Ox (+) x
— i mXe Xe)"
&
Um: 4) = | $ Sxwy € oe A
d va OX «de
@)
G) TdanAtes atbwohue Remit
Dp Na % , mesS Mm
if. a Ula aNib(nn)= EL
} As Abs {yn olen) Can Luror Chose fo
confer of mam & reloAn® cyorltresys
—& momenta (conont ccbly Con fugahe )
Rem = oe + (7+)
eS ¥=F,
> [PRS a } SS aces |e
ie + zn + UP) e (RA) ERIR A
whore eS 28 foe Dram.
row [|Sstpamble: WW. (RF) = Ni(B) PCE) i
Fete) = EatilRale Glee.
eo
Ay E = +»
(Ba UOYM=EYA) WTO aM
ze + U0) oii
I!) where es = ie = am
(/_+2 pe a a *
ae EY (a)
SAeolmsze's ESN for Hydrogen atin ,
©
W,,(8) = LIY22) ee - ‘y. (2)
=> Gremd sbte orbel pact :
ol 1 \% > fet
et eee = (rae = eC Ao
ue +2
Qi i = e
eX rt
Yoo (fi-r.) es syrrmebhic indler 1,2 ber
bucd ewerall Ks for tuo ferertans rwat
be anksyrometrfe =>
Kee Pak. puat be aX tio Syefosr ste fesof-
(AS Gant syromohrte =) sinylet
