ΔxΔp ≥ [itex]\frac{h}{4\pi}[/itex](adsbygoogle = window.adsbygoogle || []).push({});

Since Δx=ct for a photon and Δp=(mv[itex]_{f}[/itex]-mv[itex]_{i}[/itex])

Then ct(mv[itex]_{f}[/itex]-mv[itex]_{i}[/itex]) ≥ [itex]\frac{h}{4\pi}[/itex]

Since mv=[itex]\frac{h}{\lambda}[/itex]

You have ct([itex]\Delta[/itex][itex]\lambda[/itex])[itex]^{-1}[/itex]h ≥ [itex]\frac{h}{4\pi}[/itex]

Planck's constant cancels, move the c over [itex]\lambda[/itex], [itex]\frac{c}{\lambda}[/itex]=f

This leaves you with t[itex]\Delta[/itex]f ≥ [itex]\frac{1}{4\pi}[/itex]

Dimensional analysis checks. Is this correct and is there any use to this equation?

t ≥ (4[itex]\pi[/itex]Δf)[itex]^{-1}[/itex]

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# Uncertainty Principle with time and frequency

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