1 La molécule HCl en champ électrique

µ= (MHMCl)/(MH+MCl)
r0=|~rNa −~rCl|
ψ(θ, ϕ)S2
H=L2S2
hψ1|ψ2i=Zψ∗
1(θ, ϕ)ψ2(θ, ϕ)dΩ
dΩ = sin θdθdϕ
G
µ
G
r0
Cl
H
I=µr2
0
ˆ
~
L=ˆ ~r ∧ˆ ~p ˆ
H0=
ˆ
~
L2/(2I)
Yl,m (θ, ϕ)|l, mi
L2(S2)l= 0,1, . . . m =−l, . . . , +l
ˆ
Lz|l, mi=~m|l, mi,ˆ
~
L2|l, mi=~2l(l+ 1) |l, mi,

ˆ
H0
~2
2I'1.3 10−3eV
~
D
~
Ez
ˆ
H1=−ˆ
~
D.~ Eˆ H=ˆ H0+ˆ H1
D=~ DE=~ Ecos θ
hˆ
H, ˆ Lzi= 0
ˆ
H L2(S2)
~
Eˆ Hˆ
H
E(1)
E(2)
~
E
a ψ
ˆ
Aψ =aψ ˆ Aˆ Bhˆ A, ˆ Bi= 0
ˆ
Aˆ B
ˆ
H0|ni=εn|niˆ H=ˆ H0+ˆ H1ˆ Hψn=Enψn
ˆ
H1
1En'εn+E(1) E(1) =hn|ˆ
H1|ni
En'εn+E(1) +E(2) E(2)
n=Pn06=n
|hn|ˆ
H1|n0i|2
n−n0
Yl,m (θ, ϕ) (−1)l(PYlm) (θ, ϕ) = Ylm (π−θ, ϕ +π) =
(−1)lYlm (θ, ϕ)
l06=l±1hl, m|cos ˆ θ|l0, mi= 0
hl, m|cos ˆ θ|l+ 1, mi=s(l+m+ 1) (l−m+ 1)
(2l+ 1) (2l+ 3) =hl+ 1
|{z}
l0
, m|cos ˆ θ|l
|{z}
l0−1
, mi
l0=l+ 1