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1

This has been fixed in V 10.0.2. It no longer returns 0. On windows 7, 64 bit: FullSimplify[I InverseFourierTransform[FourierTransform[Cosh[t], t, w]/w, w, x]]

2

The approach using Re[] is at least questionable and even more important, not necessary. First notice how Mathematica performs the Fourier transformation. It stores $\omega=0$ in the first element of the list. The highest frequencies are in the middle. Doing something like the following results in a real valued transformation t1Lst=Table[i+ I i Sin[2.1 ...

4

For a set of data $\{t_i,A(t)\}$ its possible to define a continuous function, properly scaled, that is the Fourier transform of the data set. 1/Sqrt[n] Sum[y[[r]] Exp[(2 \[Pi] I)/n (r - 1) (s n dt)], {r, n}] Then an implementation for the absolute value of the Fourier transform could be: cxyFtM[d_, s_] := Block[{n, t, y, dt}, n = Length[d]; t = ...

4

Sektor has helpfully provided a way to numerically plot the Fourier transform of the eigenstates, as follows. First, create the matrix: Eo = 1; t = 0.2; NA = 100; matrix = SparseArray[{{i_, i_} -> Eo, {i_, j_} /; Abs[i - j] == 1 -> -t, {i_, j_} /; i == 1 && j == NA -> -t, {i_, j_} /; j == 1 && i == NA -> -t}, ...

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