The Heisenberg uncertainty principle

Statement

$\Delta x \, \Delta p \geq \hbar/2$ — the product of the uncertainties in a particle’s position and momentum can never be smaller than the fixed bound $\hbar/2$.

Why is it true?

This is not a limitation of measuring instruments — it is an intrinsic property of nature: a particle cannot simultaneously have perfectly definite position and momentum, a mathematical consequence of matter's wave nature.

Topics that use this theorem

Related theorems

Step-by-step proofs

No step-by-step proof yet for this theorem.