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Quantum Foundations Calculator

Fundamental quantum mechanics calculations. Wave-particle duality, Heisenberg uncertainty, quantum harmonic oscillator, hydrogen atom, and spin.

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Step 1 of 6

How to Use This Calculator
  1. Follow the step-by-step wizard — complete each step before moving to the next. This guided approach ensures you provide all the necessary information in a logical order.
  2. Calculation Type — Calculation mode to use. Choose from: Wave-Particle Duality, Heisenberg Uncertainty, Quantum Harmonic Oscillator, Hydrogen Atom, Spin & Pauli Exclusion. default: 0.
  3. Particle Type — enter your preferred option from the dropdown. Choose from: Photon (enter λ in nm), Electron, Proton, Custom. default: 1.
  4. Energy (eV) or Wavelength (nm) — eV for matter, nm for photon default: 1.
  5. Custom Mass (kg) — enter a numeric value. default: 9.109e-31.
  6. Uncertainty Pair — enter your preferred option from the dropdown. Choose from: Position-Momentum (Δx·Δp), Energy-Time (ΔE·Δt). default: 0.
  7. Position Uncertainty Δx (m) — enter a numeric value. default: 1e-10.
  8. Energy Uncertainty ΔE (eV) — enter a numeric value. default: 1.
  9. Particle Mass (kg) — enter a numeric value. default: 9.109e-31.
  10. Particle Mass (kg) — Mass of the object. default: 9.109e-31.
  11. Angular Frequency ω (rad/s) — enter a numeric value. default: 1,000,000,000,000,000.
  12. Quantum Number n — n = 0, 1, 2, ... default: 0.
  13. Principal n — n = 1, 2, 3, ... default: 1.
  14. Angular l — l = 0 to n-1 default: 0.
  15. Magnetic m — m = -l to +l default: 0.
  16. Particle — enter your preferred option from the dropdown. Choose from: Electron, Proton, Neutron, Photon. default: 0.
  17. Magnetic Field (T) — For Zeeman splitting default: 1.
  18. Once all inputs are set, review your results in the Results panel. Here's what each output means:
  19. de Broglie λ (nm) — shown as a numeric value. This is the primary result of this calculator.
  20. Minimum Uncertainty — shown as a numeric value. This is the primary result of this calculator.
  21. Energy (eV) — shown as a numeric value. This is the primary result of this calculator.
  22. Orbital — your calculated result. This is the primary result of this calculator.
  23. Spin States — shown as a numeric value. This is the primary result of this calculator.
  24. Momentum (kg·m/s) — shown as a numeric value.
  25. Frequency (Hz) — shown as a numeric value.
  26. Scale — your calculated result.
  27. Minimum State — your calculated result.
  28. Physical Regime — your calculated result.
  29. Zero-Point Energy (eV) — shown as a numeric value.
  30. Level Spacing (eV) — shown as a numeric value.
  31. Δx (m) — shown as a numeric value.
  32. Energy (eV) — shown as a numeric value.
  33. Ionization (eV) — shown as a numeric value.
  34. Radius (nm) — shown as a numeric value.
  35. Spectral Series — your calculated result.
  36. Statistics — your calculated result.
  37. Zeeman Splitting (eV) — shown as a numeric value.
  38. Larmor Freq (MHz) — shown as a numeric value.
  39. View the Energy Levels below for a visual breakdown of how the numbers relate to each other.
  40. Check the Quantum Properties for a detailed row-by-row breakdown. This is useful for spotting trends or finding values at specific points.
  41. Explore the related calculators below if you need deeper analysis or want to approach this topic from a different angle.
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Formula

λ = h/p | ΔxΔp ≥ ℏ/2 | E_n = ℏω(n+½) | E_n = -13.6/n² eV

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