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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 2

How to Use This Calculator
  1. In the de Broglie section, enter Particle Mass (kg) and Momentum or Velocity to compute the matter wavelength — visible diffraction requires wavelengths comparable to lattice spacing.
  2. Switch to the Harmonic Oscillator tab and enter Angular Frequency (rad/s) and Quantum Number (n) to see energy levels Eₙ = ℏω(n + ½).
  3. Use the Hydrogen Atom section with Principal (n), Orbital (l), and Magnetic (m) quantum numbers to get atomic energy and orbital radius.
  4. In the Spin section, enter Magnetic Field (T) and select particle type to compute Zeeman splitting and Larmor frequency.
  5. Read the Energy Levels chart to visualize the spacing and compare harmonic oscillator vs. hydrogen-like energy structures.

What each input means

Calculation Type
Calculation mode to use.
Energy (eV) or Wavelength (nm)
eV for matter, nm for photon
Particle Mass (kg)
Mass of the object.
Quantum Number n
n = 0, 1, 2, ...
Principal n
n = 1, 2, 3, ...
Angular l
l = 0 to n-1
Magnetic m
m = -l to +l
Magnetic Field (T)
For Zeeman splitting

How this is calculated

Formula

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

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    Calculation Type = 0, Particle Type = 1, Energy (eV) or Wavelength (nm) = 1, Custom Mass (kg) = 9.109e-31 = 16 input(s) provided
  2. Calculate de Broglie λ
    de Broglie λ
    1.2264259661581491 = 1.2264259661581491
  3. Calculate Momentum
    5.402747766957797e-25 = 5.402747766957797e-25
  4. Calculate Frequency
    241798924208491.8 = 241798924208491.8

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De Broglie λ

λ = h / (mv) for non-relativistic momentum.

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