PHQ711 Mécanique Quantique

n n ∈[[0; +∞[[ l
l∈[[0; n−1[[
∆1
r= 4πδ(r)
q r
V=q
4πε0r
∆ (V) = −ρ
ε0
q
ρ=qδ(r)
∆q
4πε0r=−qδ(r) ε0
q
4πε0
∆1
r=−qδ(r) ε0
1
4π∆1 r=−δ(r)
∆1
r=−4πδ(r)
−→
P=−i~−→ ∇()
−→
L=−i~−→ r∧−→ ∇
Lx=i~z∂
∂y −y∂ ∂z 
Ly=i~x∂
∂z −z∂ ∂x 
Lz=i~y∂
∂x −x∂ ∂y 
ϕ∈[0; 2π]θ∈[0; π]

r=rˆer
=rsin θcos ϕˆex+rsin θsin ϕˆey+rcos θˆez
−→
∇= ˆer
∂
∂r + ˆeθ
1
r
∂
∂θ + ˆeϕ
1
rsin θ
∂
∂ϕ
∆ = 1
r
∂2
∂r2r−1 r2~2−→
L2
hψ1|W|ψ2i
ψ1ψ2W
W ψ
ψ1≡ψ2
α
c v =αc
α
α=e2
~c4πε0
α1
137
α~
−→
L−→ L
−→
L=−→ r∧−→ p
a0−→ r v =αc
~=a0mαc
m
α=~
mca0
α

L(x, ˙x, t)x˙x
V(x, t)
L=T−V
T V
x(t)S
S=ˆt2
t1
L(x, ˙x, t) dt
(x1, t1) (x2, t2)
∂L
∂x −d dt
∂L
∂˙x= 0
N qii∈[[1; N]]
V(q1, q2, . . . , qN)L(q1, q2, . . . , qN; ˙q1,˙q2,..., ˙qN)
T V
qi