QNT-16

de Broglie wavelength

λ = h / p. Matter waves for a momentum p.

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Quantade Broglie

Governing equation

\lambda=h/p

$p \in \left[1, 10000\right]$

where

p: Momentum (keV/c)
\lambda: Wavelength (pm)

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

\lambda=h/p

$p \in \left[1, 10000\right]$

$p = 1$ $\lambda = 1240$

Along the curve

②

Domain of the variable — blue

p_{\min} = 1,\quad p_{\max} = 10000

$p \in \left[1, 10000\right]$

$p = 1$ $p = 1$

Along the curve

③

Response curve — green

\lambda=h/p

$p \in \left[1, 10000\right]$

$p = 1$ $\lambda = 1240$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\lambda}{\mathrm{d}p}

$p \in \left[1, 10000\right]$

$p = 63.89$ $\lambda^{\prime} = -9.781$

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-16 — de Broglie wavelength) is the form associated with de Broglie. Working symbols: $p$ $\rightarrow$ $\lambda$ . Electrons in a crystal diffract like X-rays. Davisson–Germer.

Purpose

Purpose: compute

\lambda

from

p

in Quantum mechanics via

\lambda=h/p

λ = h / p. Matter waves for a momentum p. 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

p = 100.000\,\mathrm{keV/c}

, the governing relation

\lambda=h/p

yields

\lambda = 12.4000\,\mathrm{pm}

. A particle, a trailing wave. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Momentum p100 keV/c

Outputs

Wavelength \lambda12.4000 pm

Reading speed

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Narration of this film

A particle, a trailing wave.

Electrons in a crystal diffract like X-rays. Davisson–Germer.

Reading speed

Watch on YouTube