Compute the discrete energy levels E_n of a particle in a 1D infinite square well from well width and mass, for quantum-mechanics stationary-state problems and teaching demos.
粒子在一维势阱中的能级。校验：量子数 n 须为正整数（1、2、3…），粒子质量 m 与阱宽 L 须大于 0，非法输入提示并中止；明细表与主结果共用同一校验状态。
| Item | Formula / Note | Source / Standard |
|---|---|---|
| Infinite square well | E_n = n²h²/(8mL²) | Textbook QM |
| Zero-point energy | E₁ ≠ 0 | Quantum mechanics |
| Wavefunction | ψ_n = √(2/L) sin(nπx/L) | Schrödinger solution |
| Level spacing | ΔE grows with n | Quantum size effect |
| 3D generalisation | E ∝ n_x²+n_y²+n_z² | Quantum mechanics |
| Applications | Quantum dots, nanostructures | Nanophysics |