ATM-22

Linear Stark snapshot

ΔE = e E ⟨z⟩. First-order Stark shift of a permanent electric dipole.

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SpectraStark

Governing equation

\Delta E=e\mathcal{E}\langle z\rangle

where

\mathcal{E}: Electric field (kV/cm)
\langle z\rangle: Dipole length (Å)
\Delta E: Stark shift (meV)

Lecture brief

Historical brief

Balmer, Rydberg, Bohr (1913), fine structure, Zeeman and Stern–Gerlach built the spectrum of one atom. The lab computes levels, selection and magnetic splitting. This sheet (ATM-22 — Linear Stark snapshot) is the form associated with Stark. Working symbols: $\mathcal{E}$ , $\langle z\rangle$ $\rightarrow$ $\Delta E$ . Hydrogen n=2 is linear because of ℓ degeneracy. Most atoms start at second order (polarizability).

Purpose

Purpose: compute

\Delta E

from

\mathcal{E}

\langle z\rangle

in Atomic physics via

\Delta E=e\mathcal{E}\langle z\rangle

ΔE = e E ⟨z⟩. First-order Stark shift of a permanent electric dipole. Use it when a real atomic physics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\mathcal{E} = 10.000\,\mathrm{kV/cm}

\langle z\rangle = 3.000\,\mathrm{Å}

, the governing relation

\Delta E=e\mathcal{E}\langle z\rangle

yields

\Delta E = 0.300\,\mathrm{meV}

. An atom, a static E, a shifted line. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Electric field \mathcal{E}10 kV/cmDipole length \langle z\rangle3 Å

Outputs

Stark shift \Delta E0.300 meV

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Narration of this film

An atom, a static E, a shifted line.

Hydrogen n=2 is linear because of ℓ degeneracy. Most atoms start at second order (polarizability).

Reading speed

Watch on YouTube