Model quantum waves with flexible inputs and clear plots. Track phase, density, and motion with practical physics outputs. Make wave behavior easier to inspect and understand.
This tool evaluates a plane-wave style function and related outputs for educational, modeling, and visualization purposes.
| Case | Amplitude A | Wavelength λ | Frequency f | Phase φ | Position x | Time t |
|---|---|---|---|---|---|---|
| Electron-like sample | 2.5 | 4.0 | 3.0 | 30° | 1.2 | 0.25 |
| Standing-style check | 1.8 | 2.2 | 1.5 | 90° | 0.8 | 0.10 |
| Low-frequency sweep | 3.1 | 5.5 | 0.8 | 15° | 2.4 | 0.60 |
General plane wave: ψ(x,t) = A ei(kx - ωt + φ)
Real part: Re[ψ] = A cos(kx - ωt + φ)
Imaginary part: Im[ψ] = A sin(kx - ωt + φ)
Probability density: |ψ|² = Re[ψ]² + Im[ψ]²
Wave number: k = 2π / λ
Angular frequency: ω = 2πf
Phase velocity: v = fλ
de Broglie momentum: p = h / λ
This implementation combines classical wave form structure with common quantum mechanics notation. The energy estimate uses the non-relativistic expression E = p² / 2m for an added reference metric.
It computes the real part, imaginary part, magnitude, and probability density of a plane-wave style function. It also reports wave number, angular frequency, velocity, de Broglie momentum, and a simple kinetic energy estimate.
No. It is a focused educational calculator for a wave-function form with user-controlled parameters. It does not solve boundary-value problems, Schrödinger eigenstates, or multi-dimensional quantum systems automatically.
Quantum wave functions are often complex-valued. Showing both components helps you inspect phase behavior, oscillation structure, and the relationship between the complex form and measurable probability density.
|ψ|² is the probability density. In quantum mechanics, it represents how likely a particle is to be found near a given position when the wave function is properly normalized.
For a simple plane wave with fixed amplitude, the magnitude remains constant while phase changes over space and time. The oscillation appears in the real and imaginary parts instead.
Use one consistent unit system throughout the calculation. For physics work, SI units are the safest choice: meters, seconds, hertz, kilograms, and radians or degrees for phase input.
The graph shows the real part, imaginary part, and probability density across the selected x-range at the entered time. This makes it easier to inspect oscillation patterns and compare output modes.
Yes. Use the CSV button to export the numeric summary and plotted points. Use the PDF button to save a clean report-style snapshot of the page and result section.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.