QNT-23

Heisenberg floor

Minimum momentum smear.

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GoverningHeisenberg floor

Governing equation

\\Delta x\\Delta p\\ge\\hbar/2

$dx \in \left[0.01, 4\right]$

where

dx: dx (nm)
dp: Heisenberg floor (keV/c)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\\Delta x\\Delta p\\ge\\hbar/2

$dx \in \left[0.01, 4\right]$

$dx = 0.01$ $dp = 9866.9$

Along the curve

②

Domain of the variable — blue

dx_{\min} = 0.01,\quad dx_{\max} = 4

$dx \in \left[0.01, 4\right]$

$dx = 0.01$ $dx = 0.01$

Along the curve

③

Response curve — green

\\Delta x\\Delta p\\ge\\hbar/2

$dx \in \left[0.01, 4\right]$

$dx = 0.01$ $dp = 9866.9$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}dp}{\mathrm{d}dx}

$dx \in \left[0.01, 4\right]$

$dx = 0.035$ $dp^{\prime} = -1.64\times 10^{5}$

Along the curve

Lecture brief

Historical brief

Planck (1900), Einstein’s photoelectric law, Bohr, de Broglie, Heisenberg and Schrödinger’s 1926 equation rebuilt matter as amplitude. These sheets are the first solvable models: wells, spin, tunneling, uncertainty. This sheet (QNT-23 — Heisenberg floor) is the form associated with Heisenberg floor. Working symbols: $dx$ $\rightarrow$ $dp$ . Minimum momentum smear. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

dp

from

dx

in Quantum mechanics via

\\Delta x\\Delta p\\ge\\hbar/2

Minimum momentum smear. Use it when a real quantum mechanics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

dx = 0.100\,\mathrm{nm}

, the governing relation

\\Delta x\\Delta p\\ge\\hbar/2

yields

dp = 986.688\,\mathrm{keV/c}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

dx dx0.1 nm

Outputs

Heisenberg floor dp986.688 keV/c

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Minimum momentum smear. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube