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.

What each input means

Eₙ = n²π²ℏ² / (2mL²)

Identify Input Parameters
4 parameters
Quantum Number (n) = 1, Potential Type = 0, Well Width / Char. Length = 1e-10, Particle Mass = 9.109e-31 = 4 input(s) provided
Calculate Energy
Energy = Number(energyEV.toExponential(4))
37.611 = 37.611
Calculate Energy to Next Level
Energy to Next Level = Number(energySpacing.toExponential(4))
112.83 = 112.83
Calculate Wavelength
Wavelength = Number(wavelength.toExponential(3))
2e-10 = 2e-10
Calculate Momentum
Momentum = Number(momentum.toExponential(3))
3.313e-24 = 3.313e-24
Calculate Transition Frequency
Transition Frequency = Number(transitionFrequency.toExponential(3))
27280000000000000 = 27280000000000000