Wave Function Calculator

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

Amplitude

Wavelength

Position

Time

Tab to move between fields

Probability Density |ψ|²

Real Part

Imaginary Part

Momentum0 kg·m/s

Energy0 J

Phase Velocity3,637,198 m/s

How to Use This Calculator

Enter Amplitude of the wave function — higher amplitude increases probability density at that location.
Enter Wavelength (m) — the de Broglie wavelength; smaller wavelength means higher momentum.
Enter Position (m) — the spatial point where you want to evaluate the wave function.
Enter Time (s) to see how the wavefunction evolves; at t = 0 you get the initial state.
Read Probability Density |ψ|² — the measurable probability of finding the particle at that position, plus Momentum and Energy from the de Broglie relations.

How the result changes with Amplitude

Amplitude	Probability Density \|ψ\|²	Real Part
1	1	1
3.5	12.25	3.5
6.5	42.25	6.5
9	81	9

ψ(x,t) = A × e^(i(kx - ωt))

Identify Input Parameters
4 parameters
Amplitude = 1, Wavelength = 1e-10, Position = 0, Time = 0 = 4 input(s) provided
Calculate Probability Density |ψ|²
Probability Density |ψ|²
1 = 1
Calculate Real Part
Real Part
1 = 1
Calculate Imaginary Part
Imaginary Part
0 = 0
Calculate Momentum
Momentum = Number(momentum.toExponential(3))
6.626e-24 = 6.626e-24
Calculate Energy
Energy = Number(energy.toExponential(3))
2.41e-17 = 2.41e-17