Well, the uncertainty in wavelength corresponds to uncertainties both in energy and momentum, which have uncertainty relationships with time and position respectively. However doing the same calculations using the energy/time relation yields the same result: E=hc/λ, ΔE=hcΔλ/λ², ΔtΔE=ħ/2, Δt=h/4πΔE=λ²/4πcΔλ, Δx=cΔt=λ²/4πΔλ, which is exactly what I had before. But I must be making a mistake somewhere because I know the results I get using that equation are incorrect.
So I guess what I'm getting at then, is how do I determine the uncertainty in x (ie the minimum possible beam width) from the range of wavelength values that the laser outputs?
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