Atomes à plusieurs électrons

Hel.st. =
p
X
i=1
(~p2
i
2m−Ze2 4π²0ri
) + X
i<j
e2
4π²0rij
Z
p=Z ~pi=−i¯h∂
∂~ri

1/rij
−4×13,6×2 = −108,8Z= 2
p+ 1 p
p−1
H∼X
i
(−¯h2
2m~
∇i+Veff (~ri)) = X
i
Hi
Veff (~ri) = −Zeff (~ri)e2
4π²0ri
Zeff (~r)~r
Veff ~r r

Zeff (r)D(r)
Zeff (r) = Z−Zr
0
D(r)dr ×p−1
p
Zeff (0) =
Z Zeff (∞) = 1 p Zeff (∞) =
Z−(p−1)
Veff
Veff
p
Hi=−¯h2
2m~
∇i+Veff (~ri)
ψnlml=Rnl(r)Ylml(θ,φ)
Rnl
Veff
Veff
²nl
n l 0≤l≤n−1
D
ρ D(r)=4πr2ρ(r)/(−e)

n l
n n = 1 l= 0
s
l= 0 p l = 1 d l = 2 f l = 3
Veff ²nl
ψnlml
n= 1
l= 0
ψnlml
ns np nd
nf nl
n l
²nl n+l n +l ²nl
n