QNT-24

1D Fermi energy

1-D Fermi gas snapshot.

Reading speed

Governing1D Fermi energy

Governing equation

E_F=(\\pi^2\\hbar^2 n^2)/(2m)

where

n: n (1/nm)
Ef: 1D Fermi energy (eV)

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-24 — 1D Fermi energy) is the form associated with 1D Fermi energy. Working symbols: $n$ $\rightarrow$ $Ef$ . 1-D Fermi gas snapshot. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

Ef

from

n

in Quantum mechanics via

E_F=(\\pi^2\\hbar^2 n^2)/(2m)

1-D Fermi gas snapshot. 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

n = 1.000\,\mathrm{1/nm}

, the governing relation

E_F=(\\pi^2\\hbar^2 n^2)/(2m)

yields

Ef = 0.376\,\mathrm{eV}

. 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

n n1 1/nm

Outputs

1D Fermi energy Ef0.376 eV

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

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

1-D Fermi gas snapshot. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube