QNT-29

HO quanta

Quantum harmonic oscillator.

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GoverningHO quanta

Governing equation

E=(n+\\tfrac12)\\hbar\\omega

where

n: n (—)
w: w (PHz)
E: HO quanta (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-29 — HO quanta) is the form associated with HO quanta. Working symbols: $n$ , $w$ $\rightarrow$ $E$ . Quantum harmonic oscillator. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

E

from

n

w

in Quantum mechanics via

E=(n+\\tfrac12)\\hbar\\omega

Quantum harmonic oscillator. 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 = 3.000\,\mathrm{—}

w = 1.000\,\mathrm{PHz}

, the governing relation

E=(n+\\tfrac12)\\hbar\\omega

yields

E = 2.304\,\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 n3 —w w1 PHz

Outputs

HO quanta E2.304 eV

Reading speed

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Narration of this film

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

Quantum harmonic oscillator. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube