# symmetry-xk-squared-magnitudes.mp4

Chapter section: Position / Wave Number Uncertainty

Caption (verbatim):

Trade-off in uncertainty of position and wave number

Image description (verbatim):

The squared magnitudes trade position and wave-number widths

## Before the animation

Chapter lines 1057–1059:

```math
\Delta x\,\Delta k\ge\frac12.
```

Chapter lines 1060–1060:

This derivation is rather involved, but we can get a feel for the result by plotting the squared magnitude of a wave function and labelling the standard deviation.

## After the animation