Lent raliibung am 17.01.2018

Thema : ① rehimpvls Algebra C Blatt to In Aufgabe 3)

[ hi, Lj ]

-

- i Eiji.

Li?(I 8) , . . .

[ Si, Sj ] = i E. just .

Si -

- IE;Long , pi ,

too )

Sx, Sy , Sz ; 5=5×2+5,2+5,7

[ s'

, s ;] -

. O → S'

kommotiert mit Susy , Sz

Eigenzustande :

517, uh - 717in )

Sz hanker IA, µ >

Leiteroperator en : S±=S+ ± 'S,[ St , S .

I = [ S,tis

, ,S+- is

,] = ES

+ , Sir - is,] ti [ Sy ,

Sir . is,]

= Csx.

, SD - IS , , Sy 3 + i CSy , 5×3 iffy , Sy ] = Sz -152=252- - - -=O

isz

- is,

= O⇒ [ St

,S

- 3=252¥s×

, Sy ] -

-i Ensz

[ 5, S± ]

-

- [ 5,5×3 t.is

'

, Sy ]-- O

Y

F To[ Sz ,S± ] = [ Sa

, 5×3 Ii Esa , Sy I = is, Ii ( - is× ) = IS

,tisy

= IS±

wenn Sze St vertauscht : kommutator

Else 14µs ) = AS± 14µL,

claw addie ren

→Sz C S ± 17 ,µY) ISISat [ Sz ,S± )) laws = ( S±µtS± ) 17ms

= Cut 1) ( Se 17, MY

IX.Mtr >

^

St 19, M )

us -

14, µ

- A )

OECD ,µlsfeSy2 Him )

= charts'

- Sit,

>= put - ugh

,n'F- A - µ2 ⇒ µ2±A

Max µ=s5+19,5--0 → ( S -IN 175=0 ⇒ S

. 19,52=0⇒ s - s

'C- IN

5 mit St,S

.

und Sa schreiber

Sts.

= Csxtisy ) (Sir - is, )

-

- 5×2+5,2 -

isxsytisysx-sf-S.itSz

-- i [ Susy ] =

- ifisa )5=5×2+5×2 tsz-S.es

.

- Sats

• Wir kung von S'

auf His > und IX. s'

>

5=5+5.

- Sztsz

Wir Wissen ,class S

.

17,s'3=0

⇒0=5+5

.

17,83=(552-522)/7,s

'S= (Its '

-

5)17

,s

's=) A = - s 'ts "to Bardem : 5+17,6=0

,also auch S

.5+175=0

S-S

,= 5+5

.

+ [ E. 5+3=52+52-522 - 252=5 - SE - Sz⇒ s

. St IX. s > = C S2 - S } - Sz ) IX. s > = CA'

- s'

- s ) 17µs⇒ A = 82-15

⇒ D= scstr ),A -

- s' C s

'- r )

⇒ scstr ) = s'C s

'- a ) ⇒ s 's - s und (s 's Ste )

• s istganz

- Oder halbzahlig ,L'Geht nicht , das > s

'

das - s'

ganzzahligist sein muss

⇒ s - s' EIN ; ↳ E IN ⇒ SE Iz

Is ,mY ; 84siml-scsthls.msSzls ,m > = Mls ,m >

m=S

s "

"

• s-

- I → m-

. I , - I II. IS ,Hz

,

- Itin w= It ) =L -7

• 5=1 MAIO ,-1

• s-

- Zz m=3z , Az , -12 ,- Zz

Ziel : Bestimme Nm :

5. Is

.mx/Vmls.m-hStls,s-tl=Nsls,s7ISeS-IlSiS2=Nsls,s> h

Isis ,sd=Nsls ,s ) Is Estis . Jls

.sk/Vgls.syYy--2sSeS-ls,s-ti--Ns?hls,s-kAt=CCS-uS.3eS-StJls,s-

kt-C2cs-H-Ns.hn/ls.s-k )

⇒

Nf=2sNsI=2Cs - 1) t Ng

'

NE, = ?Cs- 2) + Nst..

NsI=2Cs - k )tNs-her⇒ Nst. - Us - n )=2sC2kH ) - 2

"I=2st2ks-kCkH#C litmus - ht - CS - mthlcstm )

Definiere :m=s - k ⇒

2s-i2scs-ml-ls-mlcs-m-hj-t-2s-25-tsm-s2-s.tn-

Sims- m2 -1M

=g2ts - MZTM = s C set ) - MC Mtl )-

⇒ Nm=VCstm)( s - Mtl )

S,

S,

-_ Ln ④ Lz④ ..

.

①sn⑦sz(U ) Ise, Musume > - - Dselsnim

,'s ⑦ Dszlsaimz)

CHtass.

a) = CI toss.

) ⑦ C Keast -

- thetas,

⑦ A t xH④SztOG "

S }n④sz=Sz,sn⑦ It + At ⑦ Sase

Ssixosz = Se,sn⑤ At t # ④ Sqsz

I ④ I → mma+=j=EtI=r

11,17=11.11×011.11S

.Hin ) -

- Niko > -

- CCS. ⑦Htc k ① S

.

1) 17,312,12

I = IZi - 1) ⑦ II. I ) t IF , E > ⑦ IE ,- Z >

V

Na -

. Vcr-rtn)h# = -52'

j-

- r TT

It, -17=11

,

- E > ⑦ IE,

- I > Theft

10,0 > '

- fzk.az It , -77 - the,

-2043,23 It

j -

- O Tt - ft

Satsu

Sn④Sz=⑦ s

5- Isn - Sal