A freely spreading quantum packet
Adjust the controls, inspect the calculated response and use the reading links to place the model in its physical context.
Interactive model: A freely spreading quantum packet. Enable JavaScript to adjust its controls.
σₓ(t) = √[σ₀² + t²/(4σ₀²)]
One-dimensional free particle, initial unchirped minimum-uncertainty Gaussian. Dimensionless units: ℏ = m = 1. The plotted position density broadens under unitary evolution.
What this model assumes
One-dimensional free particle, initial unchirped minimum-uncertainty Gaussian. Dimensionless units: ℏ = m = 1. The plotted position density broadens under unitary evolution.
How to explore it
Begin with the default values. Change one control at a time and watch both the graph and the readouts. Then reset the model and change another parameter. This isolates which input produces the effect you are seeing.
The plotted values are generated from the displayed equation. Downloading the calculated data lets you inspect the numerical series or compare it with a calculation of your own. The data are synthetic model outputs, not observations from an apparatus.
Before carrying a prediction into an experiment, match the model’s assumptions to the actual system: the relevant degrees of freedom, boundary conditions, noise, losses and measurement convention. The linked articles explain which comparison is physically meaningful.
Calculated model curves. One-dimensional free particle, initial unchirped minimum-uncertainty Gaussian. Dimensionless units: ℏ = m = 1. The plotted position density broadens under unitary evolution. Default control values are used in this fixed figure.
Download SVG ↓Stretching and spatial expansion
What does it mean to stretch a wave?
Which physical quantities can stretching change?
A longer wavelength is not a wider wavepacket
How do carrier wavelength and envelope width differ?
Why a free quantum wavepacket spreads
How can a localized state expand without a measurement?
A reversible mathematical stretch
Can spatial scaling preserve every component of a superposition?
Pulling alternatives apart in an interferometer
How is separating paths different from widening each packet?
Stretching a string or solid that carries waves
How do tension, length, and density affect an existing vibration?
Stretching wavelengths through relative motion and expansion
When does an observed wavelength change because of motion or geometry?
How to check whether an expanded state remains coherent
Which recombination measurements reveal surviving phase relationships?
Explore dispersion and packet expansion
How does changing a dispersion relation alter a wavepacket’s shape?
What extra evidence would link stretching to collapse?
What mechanism and threshold would a stretching-collapse proposal have to specify?