Quantum Intuition Sandbox

Wave Panel

Free packet spreading

|psi|^2 density Re(psi) Im(psi) potential

Controls

Preset Initial width σ 1.2 Central momentum k₀ 2.8 Barrier height 3.6 Barrier width 1.4

Readout

Interpretation

psi is an amplitude, not a literal water wave and not a particle path.
|psi|^2 is what connects this picture to position probability.
The histogram uses fresh identical preparations of the same state at the current time.
Tunneling here means a packet can leak through a barrier even when its central energy is below the barrier height.

Intuition Boosters

A packet that starts tighter in position spreads faster. That is the uncertainty tradeoff showing up visually.

Even when the barrier is classically too high, the amplitude can penetrate and leave a transmitted tail on the far side.

Wavefunctions add first, then you square the result. That is why interference can create dark nodes and bright fringes.

One sample is noisy. Many samples recover the underlying probability pattern, which is why the lower panel matters.

Source Anchors

NIST Atomic Spectroscopy: An Introduction for quantum-number and wave-mechanics context.
Discussion of Schrödinger’s original hydrogen solution as historical grounding for wave mechanics.
APS tunneling wave-packet study as a modern reference for packet-based tunneling language.