Quantum Wave Function Explorer

The source initializes four hundred lattice samples. Its packet center is index eighty, the width parameter is ten indices, and complex phase advances five radians per lattice index. It divides real and imaginary amplitudes by the square root of their summed probability. This normalization does not multiply by spatial spacing. The graph shows actual initial probability samples at indices sixty through one hundred, joined by teaching lines. Move the teaching cursor from index sixty through the packet center at eighty to index one hundred. Density rises toward the Gaussian center then falls. Each plotted vertex is an actual source lattice value, and cursor movement between vertices is explanatory interpolation. The packet remains the initial state throughout this scene. This coordinate scan is not time evolution or a measured particle path. The sum of all four hundred initial probabilities is one, including samples outside this cropped graph. The source density convention is discrete probability per lattice sample, not a continuum density integrated with grid spacing. Its five-radian phase increment is per index, not a calibrated physical wavenumber. This video follows the actual source arithmetic. The source advances its imaginary array first, then updates the real array using those new imaginary values. Its spatial spacing is zero point one and update increment zero point zero zero one. Start from the exact initial packet. Consider one update with a locally painted potential across indices seventy eight through eighty two. The graph observes the resulting probability at index eighty. Increase the painted potential height from zero to three hundred source units, recomputing just one source update from the same initial arrays for every input value. The gold marker follows the resulting center probability. The gray line marks its initial probability before any update. This is a parameter comparison of the numerical update rule, not elapsed flight time or evidence of a solved scattering experiment. At potential height three hundred, center probability after one update is about zero point zero four nine six nine. The source uses an illustrative semi-implicit finite-difference scheme and zero boundary samples. Changes depend on that specific update ordering and spacing. The calculation does not prove physical tunneling, convergence or exact norm conservation. For the final scene restore the actual default potential: height one hundred fifty across indices two hundred through two hundred nineteen. Start from the normalized initial packet. Recompute the full source arrays for each of one hundred discrete updates, and sum their squared real and imaginary parts. The vertical axis magnifies the total norm from zero point nine nine nine to one point zero zero three. Advance the teaching cursor through the one hundred stored update states. The plotted vertices are exact recomputed source sums, and interpolation only connects neighboring discrete states. The norm drifts above one and oscillates; this is a property of the source numerical scheme. The page runs twenty updates per draw frame, so these steps are not calibrated wall-clock seconds or a continuous exact Schrödinger trajectory. At update one hundred the norm is about one point zero zero one five one nine. The observed drift must not be hidden or called exact conservation. The original Fire control continues running without a pause, while Clear removes the potential and retains running state. The video preserves those controls and actual JSON and PNG exports, and confines its conclusions to the source’s illustrative discrete calculation.