1 Algèbre du spin 2 Mesure du spin. Délocalisation et

◦5
b
Sx,b Sy,b Sz
x, y, z
θ y ˆ Ry(θ) = exp −i
~θˆ
Sy
exp (iα~σ.~u) = (cos α)ˆ I+i(sin α) (~σ.~u)
~u ∈R3k~uk= 1 α∈R~σ = (σx, σy, σz)
ˆ
Ry(θ)|+zi,|−zi |+θi=ˆ Ry(θ)|+zi
|−θi=ˆ Ry(θ)|−zi
|+zi,|−zib Sθ=ˆ Ry(θ)ˆ Szˆ Ry(θ)−1
|+θi,|−θi
ˆ
Sθ
y
|+zi
|+ >
z
B
AD
E
z
y
x
z
θ
σx=0 1
1 0 σy=0−i i0σz=1 0 0−1σ2
k= 1
k=x, y, z σxσy=−σxσy=iσzσyσz=−σzσy=iσxσzσx=−σxσz=iσy

θ
y|+zi
|+θi,|−θi
N+θN−θ
PAPB
N+θ/N−θ
z D E
PDPE
PDPE
θ=π/2
C2
(x, y, z)∈R3
|ψi=a|+zi+b|−zi
a, b ∈C|ψi
z=a/b
sx=<ψ|
b
Sx|ψ>
hψ|ψisy=<ψ|
b
Sy|ψ>
hψ|ψisz=<ψ|
b
Sz|ψ>
hψ|ψi
z ~s = (sx, sy, sz)∈R3
k~sk=~
2~s ~/2
P1=PC2C2
z= (θ/2) e−iϕ (s, θ, ϕ)
~s = (sx, sy, sz)∈R3
z ~s = (sx, sy, sz)
MC
MCz z ∈C
M