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Fiche de mecanique quantique 2 L3

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6 fiches de quantique partie 2 du semestre 2 de licence 3 avec tout l’essentiel du cour -matrice -oscillateur harmonique -heisenberg Equation de Schrodinger -postulats - Erhenfest - Operateurs -moment angulaire et cinetique -spin -cas helium -theroreme perturbation

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  • February 23, 2022
  • 6
  • 2021/2022
  • Class notes
  • Anders katsberg
  • All classes
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Méquanique quantique 2



Matrices définition des matrices

Att ) une matrice -

C est normale si ctc.cc
" + AK
été ? et
si [Ati , Ata ) → -

C est
diagonale si c = et

matrice
si on a une
diagonale -




ZEB A) ,
= CA BJ ,
-



ELA B) ,




( d'oda f) è=ÇEÎ



D=
.
→ Ca > = THANI [FX ) = - if
( HIT )
.



0
.

=

M




( "
é=Êo÷( Ida ? .in/--EdnEqI..0
d'

fonction d' onde
°
""

;)
=



ans
=

÷ ? ed ! ed? .edu
Mn )
-
XSLX -
x
'
)
det
Scrtlxxxvîlxixxlx > di
-
e . =


D
du et -

edit dzt . . . =


ÎY M"
f
=
*
= Y dx
Si on ne sait pas A
diagonale ,
on


suppose diagonalisable :

peut DU
Equation de Schio diriger
-




dégénérescence oscillateur harmonique
matrices
flow ( ya g.) Qly
A
,
B et c Holy ) = -

) =
Elly )
on pose N =3 et [Ai B) toi AU "

opérateur annihilation et création :




Al XD a. 121 )
[B. c) +0
commutateur
=




AI XD =
azl XD
a =
#(à + i F)
Ca at ] 1
az 1737 at
=

AIT 3)
( à .jp )
,


#
=
±



px > rect a Val
=
p
=
p
d' onde
.




paquet ( démo )
.




non
dégénéré : ai # as # az
Par def if
day À [H ÂI
-



: =
,


Ex
dégénéré :
ai az = a
3
¥ Eh CUÀY
=

donc xz =



si CA B) 0 LA et
Bdiagau À
temps ) le II =fÊm+V IM
=
,

avec , ,

BA tais Bailli ) B
ai
[ptn II ] #4=X¥miDËmÀ
=
=
"
=
,
rect .

p 0

Si ai pas dégénéré : B = bilais =
xfnpcp ,
x ) +
Imp ( p.MX ihmlxpxpx ) =
-




si les vol
p
de A pas dég alors [ BRI 0
¥ 4×2 > 1mL xp
=

px >
. .

=
+

, Courant de probabilité Eq Schio
diriger
'




de


Jlnttifml dd 4-
datant) Hat ) = Hallett )
it
f- Et En ¥ datait
-

=


Inégalité de
heisenberg
OALIB >
f- IL [A B) Il
,
eq temporelle :
daf pQ
=




Frouez ih
[xp ) = A
→ alt ) =
e-

¥ spatiale En ddInrt-VH.EU£ Kitty =

eq :
-




générateur infinitésimal Eq indépendante du temps :




ËÆ a
Ula ) =

Ilya -
=
EU


ce ICX INH KUMI valeur HE
=

arc
propre Eo =




= XCXIHY
aux) fonction de thermite
e-¥ Un ly )
=



# ann ! ) t
-




→ XIU > = xht > Qnly ) =




IyYè¥
t'"
e-
polynome
~
:
Hnlytly
-




Qp ( x ) = < xlp>
~
< xllplp » =
pcxlp >
Paquet d' onde
(a) PQptn)



eilkn-wlktttdk-sclp.at#e-iEn
=p Qp
=



Mut ) =

¥ folk )
= -




ihfzq.cn ) ,


Uk) donne la forme du paquet
÷



5¥ Qptslp ) Etats liés et états de diffusion
'

p
-




÷
puits ,
oscillateur harmonique ,

transformé de fourier particule libre

Îlp ) < plus = =
TFK nm) EC ( VL a) et Kto ) )
-
= état lié
¥
"

Mn) =
le Ntp) dp ESCH -
o ) et Vlto ) ) =
diffusion
( MQ barrière surmonté par effet
:



tunnel )

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