E_1(a=1) = π²/2 ; E_1(a=2) = π²/8 ; halving ratio = 4 (1/a² scaling)

Layer 2 — Chemistryin the nanochemistry subtree

Sympy-exact witness of the 1/a² quantum-confinement scaling. Unit natural units (ℏ = m = 1, n = 1): E_1(a=1) = π²/2, E_1(a=2) = π²/8, size-halving ratio E_1(a)/E_1(2a) = 4 exactly. Canonical oracle pins: E_1_unit = 'pi**2/2', E_1_a2 =…

Related concepts

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

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