QNT-27

Square-barrier T

WKB-like opacity.

Reading speed

GoverningSquare-barrier T

Governing equation

T\\sim e^{-2\\kappa L}

where

kappa: kappa (1/nm)
L: L (nm)
T: Square-barrier T (—)

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-27 — Square-barrier T) is the form associated with Square-barrier T. Working symbols: $kappa$ , $L$ $\rightarrow$ $T$ . WKB-like opacity. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

T

from

kappa

L

in Quantum mechanics via

T\\sim e^{-2\\kappa L}

WKB-like opacity. 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

kappa = 4.000\,\mathrm{1/nm}

L = 0.500\,\mathrm{nm}

, the governing relation

T\\sim e^{-2\\kappa L}

yields

T = 0.018\,\mathrm{—}

. 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

kappa kappa4 1/nmL L0.5 nm

Outputs

Square-barrier T T0.018 —

Reading speed

Watch on YouTube

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Narration of this film

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

WKB-like opacity. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube