Schrodinger Equation Calculator

Calculate energy eigenvalues, wave functions, and quantum states for infinite wells and harmonic oscillators.

Quantum Number (n)

Potential Type

Well Width / Char. Length

Particle Mass

Tab to move between fields

Energy (Eₙ)

37.61 eV

Energy to Next Level

112.83 eV

Wavelength (λₙ)

0 m

Momentum (pₙ)0 kg·m/s

Transition Frequency27,280,000,000,000,000 Hz

Number of Nodes0

How to Use This Calculator

Enter Quantum Number (n): 1 is the ground state, higher values give excited states with more nodes.
Select Potential Type: Infinite Square Well (particle in a box) or Harmonic Oscillator (equally spaced levels).
Enter Well Width / Characteristic Length (m): atomic wells are ~1e-10 m (1 Å); quantum dots are ~10–100 nm.
Set Particle Mass (kg): default is the electron mass (9.109e-31 kg).
Read Energy (Eₙ) in eV, Wavelength (λₙ), and Number of Nodes — the ground state has zero nodes, n-th state has n−1 nodes.

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Formula

Eₙ = n²π²ℏ² / (2mL²)

Calculate quantum wave function properties including probability density, momentum, energy, and phase/group velocities.

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