What is the Stark effect?

The Stark effect is the shifting and splitting of spectral lines of atoms and molecules in an external static electric field. It is analogous to the Zeeman effect for magnetic fields and is explained by first- and second-order perturbation theory.

When does the linear Stark effect apply?

The linear (first-order) Stark effect occurs when degenerate energy levels mix under the perturbation. For hydrogen, the n=2 levels (2s and 2p) are degenerate, so the energy correction is proportional to E (the field strength). For non-degenerate levels the first-order correction is zero.

What is the quadratic Stark effect?

For non-degenerate levels, the leading correction is second-order and proportional to E². It equals −½ α E², where α is the static dipole polarizability of the atom in that state. This always lowers the ground state energy.

What units does this calculator use?

Electric field in V/m, polarizability in C·m²/V (SI), energy output in both Joules and electron-volts (eV). The linear Stark formula for hydrogen uses atomic units internally and converts to SI.

Why is the quadratic shift always negative?

The second-order energy correction is always negative for the ground state because the induced dipole aligns with the field, lowering the system energy. For excited states the sign depends on state mixing but typically the shift follows ΔE = −½ α E².

Stark Effect Calculator

Name: Stark Effect Calculator
Availability: InStock
Author: Nham Vu

Compute the energy shift and splitting of atomic levels under an external electric field using the linear or quadratic Stark effect formula.

Stark Effect Type

Principal quantum number n

Integer ≥ 2 (degenerate levels start at n=2)

Magnetic quantum number m

|m| must be less than n

Electric field E (V/m)

Typical lab range: 10⁵ – 10⁹ V/m

Parabolic quantum number n₁ − n₂

Ranges from −(n−|m|−1) to +(n−|m|−1) in steps of 2

Enter parameters and click Calculate

Summary

Compute the energy shift and splitting of atomic levels under an external electric field using the linear or quadratic Stark effect formula.

How it works

Select the Stark effect type: linear (hydrogen-like) or quadratic (general atoms).
For linear: enter the principal quantum number n, magnetic quantum number m, and electric field strength E.
For quadratic: enter the static dipole polarizability α and electric field strength E.
The calculator applies the perturbation theory formula to compute the first- or second-order energy correction.
Results show the energy shift in eV and Joules, with a breakdown of the calculation.

Use cases

Studying atomic physics and quantum perturbation theory.
Analyzing spectral line splitting in electric fields for spectroscopy experiments.
Estimating field ionization thresholds for Rydberg atoms.
Verifying quantum mechanics homework or textbook problems.
Exploring electric-field tuning of atomic transitions in precision measurement.

Frequently Asked Questions

Last updated: 2026-07-24 · Reviewed by Nham Vu