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## Homework Statement

1)

Very short laser pulses can be produced, on the order of a few femtoseconds. (look it up.) If a laser has a center wavelength of 800nm, and lasts for 20 femtoseconds, (2*10-14s) what spread of wavelengths must it have to be compatible with the time-energy uncertainty principle?

2)

Minimize the total energy (kinetic + potential) of a particle with mass m that is oscillating on a spring of spring constant k, subject to the uncertainty principle. (The distance from equilibrium can't be smaller than the position uncertainty, and the momentum can't be smaller than the momentum uncertainty.)

## Homework Equations

1)

deltaEdeltaT=h/4pi

E=hf

deltaE/E = -deltalambda/lambda

2)

f=-kx

a+(k/m)x=0

T=1/lambda

omega=2pi/T

deltaxdeltaP=h/4pi

deltaP=h/lambda

## The Attempt at a Solution

1)

deltaT*deltaE=h/4pi

deltahf=(h/4pi)/deltaT

plugging in for deltaT and h

delta(c/lambda)=3.92699*10^28

deltalambda=7.639*10^-21

obviously this answer is too small.

my teacher told me to use the deltaE/E = -deltalambda/lambda equation to plug in for E but then I get a number way smaller :

deltaE=-deltahclambda/hcdeltalamda If using E for 8*10^-7 E=2.4825*10^-19J or 3.972*10^-38

Where am I going wrong?

2)I dont even know where to start but I know to get the minimum I just take the derivative. All the equations I wrote down are just ones that I think MIGHT pertain, but not sure which ones to use where and when ...

any help appreciated. Thanks!