How can the uncertainty relation be written as such

[Abdul.119]

Homework Statement

Show that the uncertainty relation can be written as
Δλ Δx >= λ^2 /4π

Homework Equations

The Attempt at a Solution

Ok the uncertainty relation is ΔpΔx >= h/2π , also p = h/λ , so substituting that I have Δh/λ Δx >= h/2π , then divide both sides by h, and multiply both sides by λ^2, so I get Δλ Δx >= λ^2 /2π , which is still not the same as the one given, I don't understand how the 2π becomes 4π

 

[Mister T]

The minimum uncertainty is $\displaystyle \frac{\hbar}{2}$.

 

[DrClaude]

Ok the uncertainty relation is ΔpΔx >= h/2π

Are you sure about that?

also p = h/λ , so substituting that I have Δh/λ Δx >= h/2π

I don't understand what you are doing here. How can you have Δh?

 

[haruspex]

Δh/λ Δx >= h/2π

I assume you mean Δ(h/λ) Δx, which is hΔ(1/λ) Δx

multiply both sides by λ^2

But that isn't what you did.
Δ(1/λ) is not the same as 1/Δλ. What does it turn into?

 

[Abdul.119]

Right I had a mistake in the uncertainty relation that's why I was confused. I took care of it now, thank you for the help.