Upload
others
View
1
Download
0
Embed Size (px)
Citation preview
Universite de Strasbourg
L3 – 1er semestre
Travaux diriges de mecanique quantique pour la chimie –solutions
Emmanuel Fromager et Sajanthan Sekaran
DYI
Y s)
r<>
't I
l'r '
F G
,ll a-
.!
qo
l:- tst
lw
l")R
ll:t'
v ru
PU'
F lp
Ifr
il
tt> d
rs
Pl-
v ti
o'llt
' .P -:r J:.l
I
.f- _+ 3i il
liI ,"
i Io
d' \r
' \*l ({-.{l
\ }
It
i,l ol .-: I
i,r<
' t\ '( F o
tt I l\ I :-1 (sI a f
I
s.J t I
9 I qJ B
!l ,
J5a
$rl ;-T €5
UrJ
i *,'
^'l=
;
lfF ,1,It tt , I +
P t t, .i - -./ I P
l-p rts. t
uPQ
roJ
P' Ir =...,
. ll
d -JI
-q .s' +- t. t_ I a \ .) -0 (-j rt t ) t J
tr D
f n {- c
r a.)
|r-r
f t\
x * gN
l J !-
Fr sll
to!
It -.', s
,xl
r -P 'I { !-|
__-)
I <r
. ,r-F
's
o
fl' ,
,,,e
.f ll f
F \[*
^f tr,;
I
f,It
it' I
r:l rl\ I\l
* rt,l -{
f .-Gn t
,}tr
-,1, c
flNF-
la
r
i, t=
P
f,'t
f .+l \!
t\r
pt8.
pt/r
I+r It>
o!
lo-:
{,**
'u' '
!' r -
-----J
If,
rtI t
"{ rl L---)
I I \) P h I ? i-
f ?, 3 Ifr+
P
H lX
l silh
* [ s ."[
A i I \ql ;.
asr
r-+
- {
ioi il
-i+l F ll I
ll
?.[
e!,.l I
oD It ft tr
r--1
t pr
trt tt
Nr-
F' r
f,F-
€fld
"
lioq\
El
". {.,
'
T T,
ilr)
r-{ 'rn no\ g \\
r,
f*l /s Ie
t:rlL
r)
\ri I
\s _+ vr G
i l,o I
$ln ol
iltu
,l I
o! It I 'I t
--lIr\ e (, u:J
(\t
P + q 8r1
Nr-
{'lt s q,l
dn s o+ P
rVP +
v P r.
J-c
.l) Go J f
o! ) It
JtA
P *Y.
.tlS!
:
f-bq
teq
h \+ /t t, JJ ,l qll'
S tt
I -u -c a\ )r It s.I Y t, ll
JI I l
rr.\
ll '
o.r il -t $
\ \-., i
. r ,F
'5 FF
, boL
--...-
.- i
U r
F
. t L
E-.
? Ll
:.-t
? rd
r';J
i * ;
i ji+
+ l
i"ihl
* i
rir-i
JX i'
1"-a
t=
f [Js(
.1
=i a
t \$
r$;
-ti
lS
- |
t*-l
\ :i-
lL(
l '{r
r$
$ r'i
5A
}I..L
$ Ft
l'
j r3
r{
- j-r
'-i
rG i-
S +'
\ F
.( h
5-:
-1
q- f
- f-
J-
)- +
i ;1
?b
lrt5
_> ?
{a'
- :F i
+lr^
i @ \' I \
a t-=,
h -i-
.
'f\
o J'
/^$
,i- i,
- f'.
e;Ft
F t"J
-\|ol c'I-L
*i 'i^
.igf 5FN
\-t ;L -tlr-
F'S
t (\ co _9 lt e di+ Ir. t I L.
'')
t-L3.
+., ).7
\ ..tt
t\, t\F is oi lr { i.
lr FB l- d
-! t\f r !o
r,h F
$!r' ?F
'f!.r
+t t
;., ;
sd+ ^
q_N
- a) '
r\
L-t
o i-
,tl.
,e L
ft-r
'! t, 0 ,
Z o r x t f
-$a TJ FF
|..tr-
-r
F- t
F.-
h'sr Ir t
J.rL +'S
b=r
I -l'
i t+
Nr -
r
os4
:r P
t' P N1t) 7 ]- o
;F c
F J-
a;? 0 I s I +.
tl fr ts I ls
lt I.= T{ i-
? ht I tq'
$ la
r- N s. t P { Y \ -tct' t
r^\ h
\, J.
/\ tt
l' [,
_-:_
/ VIt
tls
il o\
+o'
"l$
Lrll
d.-
--b I I
/'B Go ll o + I I
,?, [F
o\^
q *. :a r, ilO
H
itF- te lt
s- Jo- , -r- F
oG-
o \-+
F o\
-lr-
F n 6t N -.i_ n. o
,'\=
\g'
fv -+.
- lrl(i,tr
"*.J\YJ
,tJJ0dd)F-6(il *trtIJ.;
-L1(
.r*xr
1lNll.l
,.lJ+dilsito1t
€e-) '
JJ-o{,-{-
dT.$itl
I !
T"S lr,.1
G(Nl o
,{'
kl"l "=l]O
d' d'u \9
v/ llf
oO
e11
ilt6\36>l!odillFJ
-|9_1rr -tA-
rt3{n
'J\5-I-
.F)+
bl.r 1
b -F)
J
aI'91.(j:+dr[+tr's
9'siI+bdIt
'- b-J
s+ 3-'
$it-.5_J;tttYd
-ls'c-+JI
6.;raJ
.s-tsl-rs-!:Qd..
,sid-l-irl
;'r ll I
Jell
r, (JLI t-Ljl ii
4lls"Ib
In4
d!'oll\tnlt3
s-- |
rlall\I6.s,6d.,
F.1;ri*-$ 6a\,!blI dsi'.r\L*,1vr .y -
JOr*{T
\ r
s./ *
s it;j-t
EILi{o
el<Jrs'Ic{
]i
o" ll oo
-- ll s
1-'o{tn t41Ecl
l.<+, g
ll.-.lJ'
IL
\J ll
-ll rrt" ll{
t{{r"s\J
{.-I>\f,hH.>r
.+>-l-, f-(
\,,r
&T.:( .q.JJf-, t6,5t-+JIt"f\F)-s +'tic-d-t-
,JI'
q-
l1 Y
rr- 'i
t{oll s" -Ir-i
c0
Arrall.5ll o..ll(ic$ il!'T"IE,Il.ll
r4
+$r(tr.l '{. -=.
j rti \r-
,a\-,)N
1t i.:{{ql6"t:11r;S
+l -{
n
r] $ IYf 3 ++il { -i
''t
d{; T
\JqIttllll sll
il'rlLLil{f
tcltl{.lc,,llsor{
v,t9-dd
!:{\S/*-ItI'ist
*)L-.* c{]-
No--
J-'
d-.-.Cl("
..1.t[."I
..1
Irs=[ g"rl
s.o
0
0.1
0.2
0.3
0.4
0.5
0.6
0 2 4 6 8 10 12 14
a 0⇢(r)
r/a0
Radial densities [hydrogen atom]
1s
2s
1
++
.|irdr,E,N-\!F*
It
0Fr*
=yt'! ul rt \
/At \
teI( *
\od \a
\\Y\..0,$.j
sl.it+
F$--....-Nl-l (F-(\AL\l
NE.P
.ilA'(\ ''
=A.)tll
^llall[r llA-s ll-{u
cui ll ..t)\
''cil*N'd'1=Atr
st-r&-Is\6i\-d,(t
r,s
:-IJ' d'
rgtL
p i"{'{
{sbi'!i
oJdiy,r--9.t|vItAItl+)sl<J./Ft{tF+1dU
Ir(
Ti*r I
..'\I ll
ctr
-5 I
d (J-
rl\311
.$.*J.'tia't\<)t--nf.?J'iiii+.1f{o'?J:S
"5\.J50JtLsi E-J.5'5
EbFt.l
/rl
53r{J-A
No
J- rr \t''
-s 6:.
n>,St
.J -I
:3.' ,r
("s+.-i
ovl66
A66
$,
!.1
tsld
6s.h'35Jzg-.&_rc,-t
t\^C'
,rJt3Io.fni -(vbJ:So,il
'.1 ';< {=cI
d i,l'
=la!
r\ \
A.; *.ttil.rtl'll o
Lrl!-i\ttr-lc\el ,. 7,et dl
ll
1 rtd+
dl-
,{ t}@
b "5 $l ,P[hY ir;r+s-'sR
'{:-(t '
ll lt'
llx11
nt(6+)y--rtl+
*l \./
*-
ebi+N-t'tt,u\,-s,fl(JJF-
T}rN
{,'! rld$Tf'rt
F,t!(r$iid-{TT+i)lI
L!-21+t)a\@.d-tJ
+IN'.t$,*-{ts-r0
IIL
!r.d=ftr'.rt
rll{,s* l)-
J.fatF)\-i,sHIJl.+-sI-uitt
6.{vl[tlrlJIJ]L-Ji.Jl
3',
Itta!b+
I)i.{i)ts6'411)i-tg'd
\rif ild,$l}-
rtSTAj "5. ,g
. \J
cl
-:i N
le
ttl- rt
co |te,9 q
t, ltL.Sr,d.f.-t,K i r, 'Fcr,,
v o-
.tr t+'
'( .{
+tldJF"
rJts
-: h[ .
f .t t
tl,itr,c {
r.:'-
,n .:
f',(.Aa
td rd
rtJ rtl
dl ll
{_ __Jad
?)-^rr tld
"C re.C
rr ill- t5
?t lF o{t8
T ANTl4lN
rt
Tnr,-., r
c{.1 f4.
rN
\-, ,r
ia",,
$ITI
?J.'
fd \:=?'.
,+, cl,(Jfl F 1:li
f{3 ll
'. .tt
> ll -cl
fl ill I'si[ au r
?d.0t?Fir s\
,rrC d
rif rt
5rF6lYa'Ul(
tlAr
l-I
TI,tf+t>"a
0ll,l,\-U
CN
ull(ddPulE*
clr,cl.l'r|i'tJI
'-)
{
rN+l*,!.\,h?8{5
Jt-t{d'{
dtr{
tdcl.cll+Ifi\ultI!l
ssJ\./
t''t i I
+rlc{rfr
.JO
d€
1_3Vtl
tI!s-r.Lj;
)+
4\dt
9i/,
d.{JI
dt
+Jll'
o"llN
It7,
\r*Fn#=ll
0E.Jn+'o,l;iltJ.s
rlfr9\E*o.l
ro*ld
lx*
sUII{
i g + "oI
rr',f .j
rr,J
.F*uJJ
' I f
alc{fw
,_dl
s
?\,i\l+|r).t{brJa
'cll.rl= ll s)
f f!
frr-IF
Tl:
1-E'f ;Tsllllo--g
/\sll
{t.s -.0L6J)i04'6r!J
.-(- .)
.rj
j+I
il-.9
{Fc)Jrrl
[JH$.sLAIi,lLrl
llrIl(riliJ--rltr tfJllcs
ll
o-l:i-It
/AUl,{.1oiII
xi =
.r rd g
",'? {\
N)
lu
IB
^$SI"_11as(sd=
I6t
i{rr
*4r-J*l.-.
{ta
-+O
.'l'
;.{t
3<
.$t*I1t
6N€
,l+1.ll
ll.JI{rci-Fd.s\
a4\(-uJ
d :{
,__, J \ I
''3 lEl I ;*
+ ils-ll i
{ {nil{t i$1 ;l'l\] $, 'o' ( *{
ni- +{'$[ i J:+i?fl ILll $ 8li
rt A 'i j rr .{
.i-
3r i$tlrf$Ji ; )I j;r= 1o
.tJ
+rt-
-I+vl,{,\8=<
ilJtf
PJ<!.rar{j
\jjj
9vt
f,= !v-tit!r.:li: i-tI
s-^.f
J'.iS6
;o -)
L$
i$3
ull d.r
.$11dIr*ll
i:.lt,tfrt6d
hl:tH ]-
-({JtE_+J-l\J
J(!
JTcl.rs{ .J5
dl-l:J.I.ld,l-
!)rclj:U.j
I.3+
a,lds- rc{llrl
lu
-idcJ
JsLAf
sst-clcl--o-