QNT-22

Compton shift

Free-electron Compton.

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GoverningCompton shift

Governing equation

\\Delta\\lambda=\\lambda_c(1-\\cos\\theta)

$th \in \left[0, 180\right]$

where

th: th (deg)
dl: Compton shift (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

\\Delta\\lambda=\\lambda_c(1-\\cos\\theta)

$th \in \left[0, 180\right]$

$th = 0$ $dl = 0$

Along the curve

②

Domain of the variable — blue

th_{\min} = 0,\quad th_{\max} = 180

$th \in \left[0, 180\right]$

$th = 0$ $th = 0$

Along the curve

③

Response curve — green

\\Delta\\lambda=\\lambda_c(1-\\cos\\theta)

$th \in \left[0, 180\right]$

$th = 0$ $dl = 0$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}dl}{\mathrm{d}th}

$th \in \left[0, 180\right]$

$th = 1.132$ $dl^{\prime} = 8.36\times 10^{-4}$

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-22 — Compton shift) is the form associated with Compton shift. Working symbols: $th$ $\rightarrow$ $dl$ . Free-electron Compton. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

dl

from

th

in Quantum mechanics via

\\Delta\\lambda=\\lambda_c(1-\\cos\\theta)

Free-electron Compton. 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

th = 90.000\,\mathrm{deg}

, the governing relation

\\Delta\\lambda=\\lambda_c(1-\\cos\\theta)

yields

dl = 2.426\,\mathrm{pm}

. 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

th th90 deg

Outputs

Compton shift dl2.426 pm

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Narration of this film

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

Free-electron Compton. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube