Quantum confinement (1D box): E_n = n²π²ℏ²/(2 m a²) ; E_n ∝ 1/a² (size scaling)

Quantum confinement: when the system dimension a approaches the de Broglie wavelength, electronic levels discretise. Infinite 1D square well (particle in a box): E_n = n² π² ℏ² / (2 m a²). Two signatures: (1) scaling E_n ∝ 1/a² — halving…