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
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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