Quantum dots confine excitons (electron-hole pairs) in all three dimensions. When R < a_B (Bohr radius),
quantum confinement dominates. The confinement energy scales as 1/R², blue-shifting the bandgap.
Energy levels: Eₙ = ħ²(χₙ)²/(2m*R²) where χₙ are zeros of spherical Bessel functions.
This enables color-tunable fluorescence by simply changing dot size — the basis of quantum dot displays.
Left: radial wavefunction |ψ(r)|². Right: absorption spectrum showing discrete exciton peaks.