Uncertainty Relations & Wave Packets

[Pi Face]

PROBLEM:
Laser pulses of femptosecond duration can be produced, but for such brief pulses it
makes no sense to speak of the ‘color’ of the laser. To demonstrate this, compute the time duration of a laser pulse whose range of frequencies covers the entire visible spectrum (4.0*10^14 Hz to 7.5*10^14 Hz).

WORK:
I know I need to use the uncertainty relation for this problem, but in one of my prof's slides it says ΔwΔt=2π but in my textbook it says ΔwΔt=1. I'm siding with the textbook and hoping the slide just had a typo, does that seem correct?

Assuming ΔwΔt=1, w=2πf so 2πΔfΔt=1, and ΔfΔt=1/(2π). Because we are asked to calculate time, Δt=1/(2πΔf)
Δf=7.5*10^14 Hz - 4.0*10^14 Hz = 3.5*10^14 Hz
then,
Δt=1/(2π*3.5*10^14 Hz) = 4.55*10^-16 s

Is that all I have to do? The question is kinda long for such little work so I'm not sure if I'm missing something. Thanks.

 

[Simon Bridge]

in one of my prof's slides it says ΔwΔt=2π but in my textbook it says ΔwΔt=1. I'm siding with the textbook and hoping the slide just had a typo, does that seem correct?

You can see for yourself by considering where the relation comes from.

Is that all I have to do? The question is kinda long for such little work so I'm not sure if I'm missing something. Thanks.

You do have a bit more work to do ... what was the purpose of doing the calculation? Has it fulfilled it's purpose?

In general, you should always comment on the results of any long-answer question: don't just leave the number hanging like that.