Fourier methods: The Gaussian wavepacket

PIN number:

Q1:ar=

Q2:Explain how you would choose a value for L that is “large enough:”

The smallest value of L that I think is “large enough” is:

PIN number:

Q3:Chartsheet for ar vs kr:

The term with largest magnitude ar has:

ar=

r=

kr=

Central value of k =

Distribution full width at half maximum height kFWHM=

PIN number:

Q4:Chartsheet for f(xn) vs xn, fseries(xn) vs xn and f(xn) vs xn:

Where in the range (-L/2, L/2) are the values of x for which fseries(x) is least

accurate? Answer:

Why is fseries(x) least accurate for these values of x? Answer:

PIN number:

Q5:For the wavepacket with halved kw, the term with largest magnitude ar has:

ar=

r =

kr=

Central value of k =

Distribution full width at half maximum height kFWHM=

Largest magnitude of f(xn) =

I expect that halving kw will result in the following changes:

What actually happened is:

Q6:For the wavepacket with quartered kw, the term with largest magnitude ar has:

ar=

r =

kr=

Central value of k =

Distribution full width at half maximum height kFWHM=

Largest magnitude of f(xn) =

I expect that quartering kw will result in the following changes:

What actually happened is:

PIN number:

Q7:For the wavepacket with halved xw, the term with largest magnitude ar has:

ar=

r =

kr=

Central value of k =

Distribution full width at half maximum height kFWHM=

Largest magnitude of f(xn) =

I expect that halving xw will result in the following changes:

What actually happened is:

Q8:For the wavepacket with doubled xw, the term with largest magnitude ar has:

ar=

r =

kr=

Central value of k =

Distribution full width at half maximum height kFWHM=

Largest magnitude of f(xn) =

I expect that doubling xw will result in the following changes:

What actually happened is:

PIN number:

Q9(a): Picture of cells A1:N30

PIN number:

Q9(b): Picture of cells N1:Z30

PIN number:

Q9(c): Picture of cells Z1:AJ30

Exploring Fourier methods with Excel: The Gaussian wavepacket

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