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sci.particle-in-box-1D Calculator
Calculates particle-in-a-1D-box energy levels E_n = n²h²/(8mL²) and wave functions ψ_n(x) = √(2/L)sin(nπx/L). Ground state (n=1) zero-point energy = h²/(8mL²) — for an electron in a 1 nm box, E₁ = 0.376 eV, explaining why quantum confinement blue-shifts quantum dot emission.
Inputs
N Quantum
Count of items or occurrences.
L M
Linear measurement. Ensure consistent units: 1 m = 1,000 mm = 3.281 ft.
Mass Kg
Total mass (kg). Distinct from weight — weight = mass × gravity. Mass is constant; weight varies with location.
Results
energy E_n (J)
Sample size or count used in the calculation.
energy E_n (eV)
Sample size or count used in the calculation.
de Broglie wavelength λ_dB (nm)
The computed linear length.
E_n = n²π²ℏ²/(2mL²)
Sample size or count used in the calculation.
energy gap E₂-E₁
Sample size or count used in the calculation.
probability density maximum
The largest value in the dataset or feasible range.