LaTeX
\sigma_x\sigma_p\ge\frac{\hbar}{2}Variables
- σx: position standard deviation
- σp: momentum standard deviation
How to use this formula
Bounds the product of position and momentum standard deviations.
Important notes
- The relation concerns statistical spread, not instrument disturbance alone.
Quick example
Gaussian minimum-uncertainty states can attain equality.
Applicability, worked calculation, and verification
Assumptions and domain checks
- The relation concerns statistical spread, not instrument disturbance alone.
- For the Heisenberg Uncertainty Relation, every denominator must be nonzero, and the numerator and denominator must remain correctly grouped.
- State the Hilbert-space, normalization, operator, basis, and unit conventions used in the calculation.
Worked example
Gaussian minimum-uncertainty states can attain equality.
Common mistakes
- When copying Heisenberg Uncertainty Relation, keep the complete numerator and denominator grouped; a missing brace or parenthesis changes the result.
- Verify the result of Heisenberg Uncertainty Relation with a known case, inverse operation, dimensional check, or independent calculation before publishing it.
Continue the workflow
Use Heisenberg Uncertainty Relation in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
\sigma_x\sigma_p\ge\frac{\hbar}{2}. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Digital Library of Mathematical FunctionsNational Institute of Standards and Technology — Definitions, notation, identities, and reference material for mathematical functions.
Frequently asked questions
What is the Heisenberg Uncertainty Relation used for?
Bounds the product of position and momentum standard deviations.
Can I copy this formula as LaTeX?
Yes. Copy \sigma_x\sigma_p\ge\frac{\hbar}{2} or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.