- #1
Lord_Sidious
- 17
- 0
ΔxΔp ≥ [itex]\frac{h}{4\pi}[/itex]
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]
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]