Chapitre 1 Mécanique Quantique ondulatoire

~p = ¯h~ k~ k
→~ k=2π
λ
p= ¯hk =2π¯h
λ=h λ¯h=h 2π
→λ=h
p
E=hν = ¯hω T =2π
ω=1 ν
P(z)∝I∝ |A|2
→

I=|A|2
A=
−¯h2
2m∆Ψ(~r, t) + V(~r, t)Ψ(~r, t) = i¯h∂Ψ ∂t (~r, t)
∆ = ∂2
∂x2+∂2 ∂y2+∂2 ∂z2
V(~r, t) =
Ψ(~r, t) =
dP (~r, t) = |Ψ(~r, t)|2d3r
→d3r ~r
Ψ(~r, t) =
7→
Ψ1Ψ2
αΨ1+βΨ2
→
I=|A1+A2|26=|A1|2+|A2|2
|Ψ(~r, t)|2
(N >> 1)
<x>=Z+∞
−∞
x|Ψ(x, t)|2dx
∆x=√< x2>−<x>2
δx > ∆x
Ψ(~r, t)
Ψ(~r, t)eiθΨ(~r, t)
V(~r)

Ψ(~r, t) = ϕ(~r)e−iEt
¯h
ϕ
−¯h2
2m∆ϕ(~r) + V(~r)ϕ(~r) = Eϕ(~r)
Ψ(~r, t)
→ |Ψ(~r, t)|2=|ϕ(~r)|2
V(x)
ϕ
ϕ0
ϕ= 0 V=∞
E < V (x)∀x
→ϕ
Z+∞
−∞ |ϕ(x)|2dx = 1
ϕ
V(x)
→ϕ= 0