Lecture Notes Atomic and Molecular Physics - of Michael Goerz

l r
9zga\t)m,^.r"^ 4o-= %^t^ar^,l*.]&
- A&t 'c.=ztao*)*^\4,*. b
r
( *.\[*,r^-

C*
6 ). = }a (rt- *= *)
c""^-*-.^ - t)r,Qa.^04"g,
$. --z,QB
g.-
| --!3
;-: !=.a = tU
r a
?F^q* LsoA-L,--J'a 2r"\4* kJ"S.^* n"C"-'i
Lu
a--.^^)
. O
&_f* \
Lu > Z,.^oqZ * q". tt
\
P"s-'irt-,*
< ge.\-f,-^
E-""d?Fe"[*-tQo Zn-.' - A,c2 h-V
L,o.&E- Q-;rL*n,^ .,o.^
uJ+ .-.>lF tei

P.= ux-,-+"s^U-
\\>**1 d* % d.r^.'.\ L.=*'A'.* e-=$\}.
alt \
l ' "\' , 'f \ : R*,^ (r) 'X"it y)
R\*) - .^\*)- .-*t i K- ,Gtr
q\r)= Zt r\ i \
r \ \ 1 -
\
- d d
Dio B^'*.Ki" o&8* ,^to.l. ..2E-L o,-[^ a.^
q - *
\^..^ti-to"-
\
=
: z\-. _,o'a,--,
{= ,F:i
\qtt<
_tz
6* !- nrG y'^ .9
'(\ T ; a\--ffi-
A r L t e 4
l: Io-- \-^)
\,^
I"-\*\t o\\=..'.[
*A^"- U "t^\*
t,
tJL") d\- - lrorz I v (", ), f)f A.
\.oln l- -a (lra)
E= d\\ "**)"r-o\.^o t ;${\r:{.- , ok- E-*+d"Lr^LJ-\ ^-{*LL,

tuo.^-& ?.-*^.* - ESN
\ Eq"N*^"^ ^.^$ t".*l.*.t u.. [*-
.g _ + i r
lu.- !-/,\ |
>) F. - -+ . .e- .a2.
'
l\h Cr*q E
l r t - \
Uc,-d^,J.J d".^ E *+-=3lc-,^ \e
t.;iJ= '. Q-1 = -t P.
t \ \n^
\---l
-i::r._:i $
-:
JL:F"F *e't'*'ez
F = B\"''=}.*,; \-3-l*^
L€fA--\ k,.l$ t.^^,{ i,* &F* ['"?.-\L,lr "--S'
he E^t)*'\ [i' '"^-=&^*o g.
GJ o'^[=O-\'L
l\.- ,^"*i**ht& &\-"'-,.sJ "k- ilh-U\*' g'^ \iJ
*^& KJ"A"\-* J-
to'
(h/tl-l'
N.a-\ 6=\ * J* \""**|f,\^.
f-
4.\ E: + "R"tr r^J
€- ( Jt] -' 1]- -oJ + Ep{
& h\-"ot d\ 6'J.
( Qz: *.h\
E^"*'6." :..-''

, (\ \\
A4=
B""s;. \V >Y
."\ .^f &, : E".'?t*' v Y cr :
( 2 - -1 \
-- \u W)
df dv, q-^,-**\.[JJ*^ R^^=\,*/t\-*"L*oL.l.
?
7g--fu a A
.""*?rJ. aA
g.Q**--.,^\ d-= gq\f,-.= ( s.*-. )
/,:- +-'L
L.rt- U\."NJ , J..H -;"t^ ".-o\ c\r, \"* r..- J"* Gp-\L
\*4o\ %2..^1} q--,r^ o"*AL ne
[]| '-1.
.= /"'Z-" -r
q -r=* ,1. L = t^^'(t. iF )
"^ ,l.lo- FRA \..\ d*= RA[\* ei*.n^ -1"'--- S?-= r !
(n *,\l dJ"F )
E= :+ f- = - \: (fe/t) s fR 1=- Z
\^^A $*^^".1 d-i E,^*1o r,"*;&rL^
-A.E: -t-q )' + 4? "'r :'
Gtz-IF
\ ."'\ )
NdU^4-,.-A* \i$ e-i4* F-4.. \ t\o^--={.t!-)

t \ . - > F +
U.$ E'.,,.1Ff,-\v'l^n^\ \r?,^
\ = I l- s
R,o;-E\ + a Lit\f^) -x-('t+z)-:(=")1
>,'l-- {}t* - [trel'.*t=L*.-[.,-[
i*?'zv
a*: B;GF
Fi. \
''o"J
o* IuJ*A
tr El,t
LLgs=s.l\-ri
- \ \ r
\
l * . t F
t\n ecAF- C\'*'-
- 2 Z -
(6\ -z-'*
= -^
"n-ltq.rl)
z*
€ iilw,rl
:d* -RRRL"^t'^t=f U*\
^ i *&-
qrl
\ =
,[r t
R*=k-\d,-L'-.-* +
uJ n't" L-'''\Jn". a-'s'^-^^
q^L^- rft el **
t,,""^W . t*- l- )
Lr*& t--.^-Erk$
t^iqt'a -i\ oa*5-=J-.^[U]** h..a^Jkl"t
D.- t=-"-tr4*.\Lg-'[= \'t\\ z-oc'< &" R\*'6 ^^o& ' oLr-
^^:rl.A d\* UJ.A'^^\ --'t^ q"{,.^-[L (*l D''\"^^-'^"^f tsZt" €)
fX" t*f,*^5,-*"\' td ^\- *id* J'+ t6+
,Fi X \\

F= = -* \t *\s\
E> ql\\
\-- 4
\- z-
-) L=e bqi.J- L*t. B 'Xi Aa 'R
!-t=*^L-**
l \
a E :
*l '*.i-4
d* L*lf - trL!*- c\.
l1
' t .
\ /
, \\\ +,\ t:(:n-") - a({+,r)
T
2\(it"r1
,/
1.\l* GJ *^F-"t ^..J oq \t-.*=j,- b"i.j"q$+
*fo-\=J.."= L',^.---..*"-
A=- Xn .f \t\ = 156;)
r ,J de \*-^*1-^*- Ll
t&=
*^{ i^
a*,- b*-*JL*\.2*,"*{*-F^-*L *i
a; 'fs'ts
E^r--1lo^;v€i- E""q,-, =9.l.*.\
E*re: E^.o.i. {.f F(F+^\
A= F -= \*\
*-J
\
1-<
o\^^-J d; {\o,-f- - L\)
r

;-\
{ - /
. n l
k -\=--L * \*=*",L
--_.t
, f
ge"J
lr:l L'1
Ig ---*
--t- -.-
I
I(
E[+i.-t g
A*+t1o*M,^*\ :-^^
'?.rq.[ Td'L=\ *LL
T l
\".-pa"Su
-) t{"*^ r+rs.i6 Dq.\r-*." ,.J P* Lo\* *-t cb',- .t,*
l-Lu.^^o3^o" eQA A; t*[\
F - - d.13-A q
\* t_-,----__
rrf o\^{'.t1'".ot.
:) sreJ^g LL== "- [ !pi^
u-s.\^I
SpL* *J.l.lJ Ai- tU&L D*L;.^t*x.tL
r\q
t-\^r
I
*J. t
\e\ = /;l;
S*
-a t"= '\
\
o\o= u^"*, spi.^--.^..*{
.r\"- 15K-...^^.6Ji:.,[*o^
duo F
: \
\t-l,;i.-J^,=
\
:

R.Aus.LI
frt**, \d.-. E^*-u-* J"-
tr:L..0_\.^
f\., 1tr,L[t" 1-*.o1. '.*
Eq\$..*.-
\ \',)- !\ e
& **1.-r,

\= R.U'. ^.-t-^^-
(,Ld*-,=& G=^a * ^^.'.JA
*xq-L t
-) E= uAJ c^^ A\="L'^,^, -S'k,*J*^4. 4-=u $i"t{
etr- ?- s
A.^= aI- t\,JA,r, {"*.tr-J\,-t-t ?L^,r-.+. Eq, L\--^.-
^fr" : I \[
('.r*, ,-*I -^& A* {*\*=^lt\)
a^-;. FJ"\"\t*^" *^l\ o\"^^="l-t- 0"*"*L-[h- (', l, u ) t,--,c'\
d-J d"L 1"-.\"+- lll-tL-lnk* ^tt L*=16.f,
"**,lrzk^I
.naa.r+=a & ?t t.-;*-[=tJ]t& **t s
l''.-L-Lk".^*^ f , )a
\-*o[.*.]^* ?x^- F.**\L ot'= 55J-^=
X- 1.!t^\ - L' t)) h= =- + ^
xr: .)1t^1 l'{s:-7\
n(z)
)cb---
#txt t^) - x (z) u rJtzl - r( ("1 Ks: o b
"T.fuS - ?-+'i
*\t-tr!."S- L=L;u
r

N- kJ*^+J
?_".^tt
- ?d*gg
,J {"-..- }k-:16,(s,},,f ,E,h,r.)-x*..(> *=\
h,- cF*t^*lS-L-\Ju d.n,o= S,g.\*=, ,,^^:[ *-;**- u.LU***
;+ ip^*no- J'=1g*,^-l-"=*
K?r
\Lk-=La h-*-,- Beth"*.
[ ..J [ \,i.. r, N, o-.=J-Q-\
T)-,2 n^^:\ enl'F,-*- t-\'\* Ul-J. &.{u^ *=A.-J. o-t-tl
9i.* -
8..
t'!.1
J",. r\*,^A=.L futjo , .L= f^-A-t"t*
P."'-&oL Til-^*,="^t\
qiJ.
S?".- *^J-'-
T*
\-;a^-\".-.L eia,
rN-
p.t=,r
'f '..t - n, ^
tu'^-- 'or^
Ht'-T$l:*"tr4
L\"-I=..[^^ Nr*[ d\4 6\L

U*\..-R,.\
-Nl[***l-
%\"-\:-.u*Ja {,",,-)
E*=.h.u. |11 S\
t*Ai ts'U*t'\ ?,'"\ F.t').nt^\ ' r i
\c^-e^ n^c. o[^ -,-'
Jz* X-' ?^+u,
&I*** &= Ro
:4 t,'") *
B*&-*4 o[= qs-:tJ-l}. P"\*\.
[-:, ', - {.= Ei"lJ; U", u0q Fe.
U^.gU.,\ \re^^ y,t *t
{*}ir
R r\s
Lntt-Cf c"^ F;
..\ N saL\.,*^ t<
\ \n't(..f A-.1
Lu-,*L-r ^^-A a.-- F

L>L.=Ic^A;,il^i+ Ta.
Bu -= B"--\c"- L"CR'U-/ "1"-" f,1,-=*,t[.^
Et=- tao: A* E,^^l.'=:o^^ ( =h^^^h-I)
l!= Ei-^L&q-J. $r-UL.^--=-t*p) *J }a\c o&^-r{"
aR> s^: Si.,{ H^J* ---Jt:t+ t
:f*t*
Et-
E'^&si* Lo^^^ "[*I.-{-t= ..*f\*L
- . H i l
iuX-:A,\i
| '\ /
'kt d-
. t
Abs'.,-f\o*
#
\, t+t")
B" - *t,, (P\
t^\[': B,r. . *o (e)
: rn-(r).[-rr
:*- E^\.**- Ql- / {a
1
oL- U\1r^1
X.^"I23*i&=a^J*-.,1. "-{
-= L.-,*'i s=."o^^
h\ : B:\' r.ru (v) ' N' + Aq 'N.

t^* cl".
a:.-a.-;
^J.lr-.a
"4.S \$;
)
:
B1-
A t l
Cs.t^.[n^"^\ b. *
jt*
l.tr \"
N ' : \ e
"tg \)j =
\.o
\f
ou
Ji.'In
- ae /iif
e-o-\ oB A
6-t
-il
U^* \}-Iel.},--.t
.+
/B.\
k-{.lR^$(.\"/rn)
Br. n'\v
,\ 4' *-o-o=
k-\.r"
7
D". \*,{L} *a$U\
2 \+ A (r.l.l x_
B"="!x,^g+*LU /" &{:*^-
A
__--
€-**t
a
+_
Xl.
-4
-\o,ztf
-e
. r \ \
!.^{*.\tL U*\.--
a
r---->
d\ r[. B\.8\,. L \>\
Bo\.,3
=
ta.A &- ?.\l A"- Vr*]o'^c- i^'^ J^iq-"- \-\&
U-\..\ o^^e*oL*." L==^ ::-L ou
d*^ \r.**L&I ;\ A,- R-*--.1 !' ^^.
>J;^^-U-.I^ f)ig",Q= P = 3=fu -\ '
F
A ,/i ur
/ /
/ / ^r-_.-_+
/ /
/ /
- Cll"= p.- \"L.""^ .r,.1 Ftel^r^a --14.,..{p
LJ,^-\*,(Au--L ,L^J
"^tH,* t}.^,-,\ p.l^.-
r\t
FC.. U U\\_\ E=)F..
*i*J. u; [,t **^agr"rqr.E-4"*J f\ "^:\ /t- E'*.-"+' ,aS*J h;\
,tk;* /" eF
q,ie!*lt\oN
njrcn^ l.-.\-,1..*I*.- +^ =F-'l-^.- E^ is-=ic.-
-\4

D*-^'.\ .q*\)
< P.1; :
tl (P1) =
A\- ? 3
, l
'^"L d\* E-=\*^L{kr--\ Ap e*=' do* \J*&.1"
. r l
cx
3 \lr6i \rt,l
\_
N
A*=.-"\\*.%L
A,l*'\..>
l.
*.F
m \sti r
\ "1"!
f ( *oU^i^r..^ ro'F-
a-F"*^ sktUa$u1
e\3-- S\.,*I-L-3= -
,.^;$i
th,'n)*: f S Rqln rts$. t e$ J't^ .9 .o D J ?z
/.t,
.r ,\
>-q. oi u" .! .og D ,t ""'n
S -*', , dr
u,^"I (r. ,lrLQ* f=o
PoL;=;}"= t^,$
i / r
th\). ! \nu )r
n 2
: ? \Yt,
o
[\t.=.t'
) n
\ r\ri
\tr^^:
crj[ s*z Jrv
?E
\e )
o
I
I
IP
I
I
!
F

Dq^-"'^^t= *%rL^ r-.-}* da thrJ* A-='"-UI*€L
At^
Atr^
:
=
a t - t
&E
-.). S= g,
R.t
j \
otr[ti
-= c)
t A
o
-\,- -- rn
"ca\
t!A
4
a,LL grQ';=,""L= LLa+
\iJJ
A ** g-b; ="*fo=
\i "J \ v')*'r-'-
t-.,.=;*
9iJ ,..tL
Ar^r oL.^" B-LL=")''$tq'-^1
,-\**[;.ILA
?*H.\ bos;42^
as^^ s{-?rQ"S- :*= T;pL$-Sig=L.
&-
o\; l-=*,-.LQ*-gA ( 5 L *=)
>P+*-8.\*-hu"a
; q-. : LrJ,"r."l^";LJ.lcA {t" *N*-\.\'.';en^
aF- -
frcrac>se

Sz^l*\ur
tte".\b-{\".
") a*^==\-^LL-t
"u
e-
_____+
{
!4^ I L*AL^\
r.Lti(a s-c.)
F.\.\'-..^ *^,.-J..0"
..* C.*^L:{.QA d* =J.-** ZI^.J*^ -
,!-n.r* \^^-l-; *;*-{.4 Sf"\,[*^ qi^=-
L.-*r.{.Qi2E
t**.,
\> $-
t) &"^U+*-*liot^ uaJK-*L\\
Dk tlo*g,=\*\L^ "d tr-&U,--*.1\o,.*(.-2g
Ai*._ d* L"rr^ o_ " Bd.,^ J-^.'..I[[!.0- o.^_[- -hrr
\'El'
i,^ ,(,_
L*rUn^i^r.-o.-+ r-i.I *^\e-.^\ *^",U;n-[ , & .l*","-\Lid..,*i.
Ji. /..t ,{"^";^,-J".--J L+
As='"$*" \,".t ****t
t")"-," [Le*\6.=\*[L.^\ .,{,^-J L)...< aI-J.\ \-^ L*X^-
tA{- 1 "-'A ',L* St-\0.*t,[':$-,.^\ >".,^eF d-o-* *"f.JoL[a,^?f
g A\"="[""&.1-* *5-L"G=,].^-*L er*+
P(-): r"- c/^*
l:,A=* o
-)
l-'/
lY d* ,=^T*t
o. .r[- A-.'lu
/*rrl- *- *\\*..q^
!.**o t*^ !$r.^^\..u Jka*-* ,,.^"[ ,t\e.$-=
\.." [q]*l
neJE=LU^L^
1LA uin^o^ L\*^ ch-ft"-=.0,.;S

A*Fcr'-
\* Q'ln^q^'^ tt'I-'J L"-'^S "''^{ J*q' EIU '
-e\"-[.$;N. {\eAg1^^-.-\ uJ J-'otrJ u-'t" Ao-h'-
d'* trJ-\p^ i-.^:=;*.!
Eu* - \- ., (E,-- E^ )
Lte.-="1*: g
.lc=--\-**,"r.- U{J*.L
El"\^\'*^,* -.}* L L"^J.*l

F.= \o\.. AU=*\.- =L.-.\,- L* {r. "}.-=
urCI-la^o^ -.^t
M-==.^-1 L bl3^ ",-,eUte"^-ru
1o.\:2,L*t
"**)
Sd**.t
o-.J-.--\
) dac: d.--,)
kJ*h{ .\--.,-t\*J =J*.
D* B.'.&.*.^S=;*L* .lo= U- *$*^^^l\i*\ Lo,^^^ {* a";
trd-t"$=k-t[.^\. '9 =e^:^ \
I
.!