Spherical Harmonics & Angular Momentum Cone
Quantum angular momentum quantisation — cone precession & |Y
ℓm
(θ)|² polar density
ℓ (orbital quantum number)
1
0
1
2
3
4
m (magnetic quantum number)
1
Angular Momentum Cone
Polar Density P(θ) = 2π sinθ · |Y
ℓm
(θ)|²
|L| = ħ√(ℓ(ℓ+1))
1.414
ħ
L_z = mħ
1.000
ħ
θ_cone = arccos(m/|L|)
45.0°
from z-axis
Missing L⊥ = √(ℓ(ℓ+1)−m²) ħ
1.000
ħ