Quantum Numbers Calculator — calculate quantum numbers with the correct physics formula. Worked example and unit notes included.
A quantum physics calculator covers three foundational results of modern physics: the de Broglie relation (matter waves), the photoelectric effect (Einstein's 1905 Nobel Prize result), and the Heisenberg uncertainty principle. These are core topics in A-level, IB, and undergraduate physics and form the basis of modern technology from electron microscopy to solar cells.
The de Broglie relation λ = h/p assigns a wave nature to every moving particle. The photoelectric effect equation E_k = hf − φ describes the emission of electrons from a metal surface when illuminated by light above a threshold frequency. The Heisenberg uncertainty principle ΔxΔp ≥ ℏ/2 sets a fundamental (not technological) limit on how precisely position and momentum can be simultaneously known.
de Broglie: λ = h/p = h/(mv). Planck constant h = 6.626 × 10⁻³⁴ J·s.
Photoelectric effect: E_k(max) = hf − φ. Threshold frequency f₀ = φ/h. No electrons emitted if f < f₀.
Heisenberg uncertainty: ΔxΔp ≥ ℏ/2, where ℏ = h/(2π) = 1.055 × 10⁻³⁴ J·s. Minimum Δp = ℏ/(2Δx). Energy-time: ΔEΔt ≥ ℏ/2.
At everyday scales, matter-wave effects are negligible — a 1 kg ball at 1 m/s has λ ≈ 6.6 × 10⁻³⁴ m, far smaller than a proton. At atomic and subatomic scales, however, λ becomes comparable to atomic spacings (0.1–1 nm), enabling electron diffraction, scanning tunnelling microscopy, and electron microscopy. The photoelectric effect explains why solar cells work only above a material-dependent threshold frequency, and why photon energy (not intensity) determines whether an electron is emitted.
Quantum mechanics formulas are standard results from the Schrödinger formalism and are sourced from NIST CODATA 2018 fundamental constants. This calculator is for educational and illustrative purposes only. It uses non-relativistic expressions, which are valid for particles with kinetic energy much less than their rest-mass energy (≪ 511 keV for electrons).