Schrödinger Equation vs Quantum Tunneling: Which Quantum Wave Simulation Should You Use?
Both simulations solve the 1D time-dependent Schrödinger equation for a Gaussian wave packet, but Schrödinger Equation is a broad explorer of six different potentials, while Quantum Tunneling is a focused calculator that measures exactly how much of a wave packet gets through a barrier.
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⚡ Quick answer
Both simulations solve the same underlying equation — the 1D time-dependent Schrödinger equation for a Gaussian wave packet — but they serve different purposes. Schrödinger Equation is a general-purpose explorer with six potential presets (infinite well, finite well, barrier, harmonic oscillator, double well, step) using a finite-difference solver in natural units, letting you watch Re(ψ), Im(ψ) and |ψ|² for many quantum phenomena. Quantum Tunneling is a focused calculator: it uses the split-step Fourier method with real eV/nm units and four particle presets (electron, proton, alpha decay, resonance), and it reports live numeric Transmission T and Reflection R so you can quantify exactly how tunnelling probability depends on barrier height, width and particle mass.
📊 Schrödinger Equation vs Quantum Tunneling
| Schrödinger Equation | Quantum Tunneling | |
|---|---|---|
| Numerical method | Explicit finite-difference (FTCS) time-stepping on a fixed 1200-point grid, in natural units where ℏ = m = 1 | Split-step Fourier (spectral) method, in real physical units of eV and nanometres |
| Potentials available | Six presets: infinite well, finite well, barrier, harmonic oscillator, double well, step | One shape only — a single rectangular barrier — with adjustable height, width and position |
| What the presets change | The shape of the potential itself (well vs oscillator vs step, etc.) | The physical scenario — electron vs thin barrier, proton vs thick barrier, alpha decay, or a resonance-tunnelling setup |
| Quantitative readout | None — purely visual; you judge tunnelling and reflection by eye | Live numeric Transmission T, Reflection R, and a classical-physics comparison T, updated every run |
| Wavefunction display | Toggle buttons switch between Re(ψ), Im(ψ) and |ψ|² one at a time | Plots |ψ|² and Re(ψ) together alongside the barrier V(x) in a single view |
| Controls | Potential dropdown, momentum k₀, width σ, and potential-height sliders | Scenario preset plus energy (eV), width σ (nm), barrier height V₀ (eV), barrier width d (nm) and barrier position sliders |
| Best for learning | A broad, qualitative tour of quantum wave behaviour — bound states, oscillation, reflection and tunnelling — across many textbook potentials | A quantitative study of how barrier height, width and particle mass control tunnelling probability, including resonance tunnelling |
Schrödinger Equation is the generalist of the two: it lets you launch the same Gaussian wave packet into six different landscapes and simply watch what happens. Drop it into an infinite or finite well and you see standing-wave-like reflection; drop it into a harmonic oscillator and it breathes back and forth; drop it into a double well and you can watch it slosh between the two minima; set the potential to "barrier" and you get a qualitative first look at tunnelling. Because the solver runs in natural units (ℏ = m = 1) on a fixed finite-difference grid, the emphasis is on recognising the shape of the wavefunction — its real part, imaginary part, and probability density |ψ|² — rather than on reading off precise numbers.
Quantum Tunneling strips away every potential except the barrier and turns tunnelling into something you can measure. Using the split-step Fourier method — a spectral technique well suited to smooth wave propagation — it works in real eV and nanometre units so the sliders correspond to physically meaningful quantities: how many electron-volts of energy the packet carries, how tall and wide the barrier is in nanometres, and where it sits. Four presets (electron, proton, alpha decay and resonance tunnelling) preload realistic combinations of mass, energy and barrier geometry, and every run reports live Transmission T, Reflection R and a classical-physics comparison T, making it the sim to reach for when you want to quantify exactly how tunnelling probability responds to barrier height, width, or particle mass.
Want to explore more? Browse the full library of 1000+ interactive, browser-based simulations, or see other side-by-side comparisons.