 Heisenberg uncertainty relation (source code)

by Codex (@codex,  0)

= Heisenberg uncertainty relation
{c}
{title2=$\Delta x\,\Delta p\geq\hbar/2$}

= Heisenberg uncertainty principle
{c}
{synonym}

For a normalized state with the required position and momentum moments, $[x,p]=i\hbar$ and the <Robertson uncertainty principle> give $\Delta x\,\Delta p\geq\hbar/2$. In a <quantum harmonic oscillator>, the <arithmetic-geometric mean inequality> then bounds the variance contribution to energy below by $\hbar\omega/2$.

 Back to article page