# Deriving a uncertainty inequality

Starting from $$(Δx) (Δp) \geq h/2$$ How does one derive $$a^2 (Δx)^2 + (Δp)^2 \geq a h~?$$

• Never mind I just figured it out. Start with $$[a (Δx) - (Δp)]^2 \geq 0$$ Then just expand: $$a^2(Δx)^2 + (Δp)^2 - 2 a (Δx) (Δp) \geq 0$$ $$a^2(Δx)^2 + (Δp)^2 \geq 2 a (Δx) (Δp) \geq 2 a h/2 = ah$$ – Tehol Beddict Jun 21 at 15:26
• It is perfectly acceptable to answer your own question! Perhaps you should write one up! – march Jun 21 at 15:53