(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider a particle in an infinite square well of width = 1. The particle is in a state

given by:

Phi=A(1/2-|x-1/2)

a=1

b) Find the general form of the expansion coefficients (the Fourier coefficients, right?)

for expanding the function in terms of the square-well basis set.

c) On the same graph, plot the wave function and the expansion in terms of square well

functions (take the sum to at least five terms or so) to verify the notion of expanding

the wave function in eigenstates of the well.

2. Relevant equations

a_n=1/L *Integrate[f[x]*Cos(n*Pi*x/L),{x,-L,L}]

b_n=1/L *Integrate[f[x]*Sin(n*Pi*x/L),{x,-L,L}]

f[x]=a_0/2+Sum[a_n*Cos(n*Pi*x/L)+b_n*Sin(n*Pi*x/L),{n,1,Infinity}]

3. The attempt at a solution

I ran through the generalized form for a_n and b_n and got the following values:

a_n=2*(-(1/(2 n^2 \[Pi]^2)) + (-1)^n/(2 n^2 \[Pi]^2)) Cos[2 n \[Pi] x]

b_n=2*((-1)^n Sin[2 n \[Pi] x])/(2 n \[Pi])

I got these by splitting the transformation at 1/2 and rewriting 0 to 1/2 as A(1/2-(1/2-x)=x and 1/2 to 1 as A(1/2-(x-1/2)=(1-x). When :I graph my final transform it lines up nicely with the right side of my phi but not the left. I know I'm missing an a_0 but I can't explain why it is so off for tho 0 to 1/2 portion.

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# Problems with Fourier transformation: jump at discontinuity

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