Potentiel quantique constant Les points du cours à

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ψ(x, t) =
ϕ(x)exp−iE t
~
ϕ(x)
~
J=|˜ ψ(x, t)|2~~
k
m×
AJ·s
A~
˜
ψ(x, t) = ˜ϕ(x) ˜χ(t)
˜χ(t) = e−i ω t E=~ω
˜
ψ(x, t) = ˜ϕ(x)e−i ω t ˜ϕ(x)
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−~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
˜
ψ(x, t) = ˜ ψ0e−i(ω t−˜
k x)
˜
k
∆p= 0
∆x→ ∞
∆p%
∆x&p
˜
ψ(x, t) = Z+∞
−∞
˜
A(p)e−i
~(E(p)t−p x)dp
E(p) = p2
2m
Z+∞
−∞ ˜
ψ(x, t)
2
dx = 1 ∀t
˜
ψ(x, t) = sin (k x +ϕ0)e−i ω t
k
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λd⇔p d
ch
`≈1 cm m≈1µg
τ≈1 s
A
A=m `2
τ≈= 10−10 J·s
E= 13,6 eV
λ= 100 nm
A=E λ
c≈10−33 J·s
m= 10−15 kg
1 mm ·s−1
ω(k)
vg=v
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˜
ψ(x, t)
(Ox)n= 5×106mm−1
Ec= 5 eV
˜
ψ(x, t) = √n e−i
~(Ect−√2m Ecx)
m= 10−15 kg `= 1 µm
τ=2m `2
~
τ
τ= 2 ×107s
<x>= 0 <p>= 0 ∆x∆p
I(λ) = Z+∞
−∞ x˜
ψ+λ~∂˜
ψ
∂x 
2
dx
I(λ) =< x2>−λ~+λ2< p2
x>
I(λ)λ
∆ = b2−4a c ≤0
Ox
˜
ψ(x, t) = ˜ ψ0ei
~(p x−E(p)t)
p0∆pp0
˜
ψ(x, t) = Z+∞
−∞
A(p)ei
~(p x−E(p)t)dp
E(p)
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