Potentiel quantique constant Notes de cours - Alain Le Rille

x∆x
pxOx ∆px
∆x∆px≥~
2
~=h
2π= 1,05 ×10−34 J·s
m= 100 g v= 2,0 m ·s−1
Ox
B∆x x ∆pxpx
m≈10−31 kg ∆x≈
10−10 mω≈1017 rad ·s−1
Bpx∆px
J·s
~
Ox ˜
ψ(x, t)
◦

x t
Z+∞
−∞ ˜
ψ(x, t)
2dx = 1 ∀t
g
gm=Z+∞
−∞
g˜ ψ(x, t)
2dx
xm=R+∞
−∞ x˜
ψ(x, t)
2dx
˜
ψ(x, t)˜ ψ(x, t)ei α
˜
ψ(x, t)m
i~∂˜
ψ
∂t =−~2 2m
∂2˜ ψ
∂x2+V(x, t)˜
ψ
V(x, t)
V(x)
Bb H
B˜ ψ(x, t) =
˜ϕ(x) ˜χ(t) ˜ϕ(x)E
B˜χ(t) = e−i ω t
BE ω
◦

˜
ψ(x, t) = ˜ϕ(x)e−i ω t ˜ϕ(x)
−~2
2m
∂2
∂x2+V(x)˜ϕ(x) = b
H˜ϕ(x) = E˜ϕ(x)
E=~ω
˜
ψ(x, t) = X
n
cn˜ϕn(x)e−i ωnt
E p
•ν ω E =h ν =~ω
•k λ p =~k=h c
λ
Oz
B∆px
d
Bθ
◦

dθ
~
ki~
kd
z
x
S1
S2
M
z
x
D
◦

S1S2˜ ψ1
˜
ψ2S2S1
BM S1S2
Ox V =V0
V0
B˜ϕ(x)
B
˜
ψ(x, t) = ˜ ψ0e−i(ω t−˜
k x)
E > V0
˜
ψ(x, t) = ˜ ψ0e−i(ω t±k x)
E < V0
˜
ψ(x, t) = ˜ ψ0e±k x e−i ω t
Ox V =V0= 0
E > V0= 0
b
H=−~2
2m
∂2
∂x2+V(x)
B
◦