Quantum double slit
Explore interference and build a finite detector pattern from reproducible single hits.
About this tool
The valid probability profile is visible immediately. Geometry, coherence, N or seed changes start an empty trial; sampling remains explicit. Start accumulates up to N hits at an illustrative 500 hits per screen second, or repeats a completed seeded trial. +1 and +100 add bounded batches. Pause/resume retains the exact sequence; Reset clears hits and keeps inputs. Options contains the window, N, seed, envelope and schematic. The envelope changes only drawing and preserves all hits. Reduced motion generates the chosen sample immediately. Only exact input texts and checkbox choices persist, including unfinished/invalid/comma drafts; legacy numeric settings migrate. Generated profiles, hits, counts and playback are never saved. Reload or navigation returns to the live profile with an empty trial.
This is an ideal scalar paraxial Fraunhofer model for two identical, non-overlapping uniformly illuminated slits: I(y) ∝ sinc²[πay/(λL)] cos²[πdy/(λL)]. d is center spacing, a is slit width, and sinc z = sin z/z. Incoherent mode removes the cosine factor and retains the single-slit envelope. It represents mutually incoherent paths or fully distinguishable path information; it is not a simulation of a measuring device or a claim that a conscious observer changes the result. No particle trajectory is calculated.
The approximate fringe spacing is λL/d. The displayed ideal local contrast is 1 or 0 before the envelope and finite detector resolution, not a contrast estimated from the finite sample. The finite window −ymax…ymax is divided into 160 cells. Composite Simpson integration with at least 32 subintervals per fringe gives each cell its probability, then probabilities are normalized over this window. Every shown hit is conditioned on detection within that window; this does not predict absolute transmitted flux or collection efficiency.
The blue density and dashed envelope share one normalization, so they can be compared directly. The gold count bars use the same cells as the sampler; their blue expectation is N_done × cell probability. The strip shows cell positions with decorative vertical separation, not a second spatial quantum model. A CDF and Mulberry32 seed make the sample independent of frame rate and chunk size.
If fewer than eight detector cells cover one fringe, the theory view shows cell-averaged density and a resolution warning. Narrow the window to resolve the pattern. The full-aperture Fresnel estimate (d+a)²/(λL) above 0.1, or a phase discrepancy above 0.1 rad between the paraxial path and geometric angular path at the window edge, triggers an approximation warning. These are practical indicators, not rigorous error bounds. No Fresnel propagation, vector effects or large-angle accuracy is provided. Sampling remains an illustration of the stated approximate formula in warned cases.