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Hello, I have a question about the following problem:

Given a wave equation [tex]\Psi(n,t)[/tex] where t is the time, and n is an integer. What is the fourier transform?

I'm trying to reproduce this paper: One-dimensional Quantum Walks by Ambainis et al. (http://citeseer.ist.psu.edu/old/514019.html"), and here says that the spatial fourier transform of such a wave is [tex]\widetilde{\Psi}(k,t)=\sum_n \Psi(n,t)e^{ikn}[/tex], without a "-" minus sign on the exponential. Why is that?

The fourier transform is defined with a minus there!! Or am I missing some property?

I am no expert in fourier analysis but can we interchange the use of the signs between the transform and the inverse transform?

Given a wave equation [tex]\Psi(n,t)[/tex] where t is the time, and n is an integer. What is the fourier transform?

I'm trying to reproduce this paper: One-dimensional Quantum Walks by Ambainis et al. (http://citeseer.ist.psu.edu/old/514019.html"), and here says that the spatial fourier transform of such a wave is [tex]\widetilde{\Psi}(k,t)=\sum_n \Psi(n,t)e^{ikn}[/tex], without a "-" minus sign on the exponential. Why is that?

The fourier transform is defined with a minus there!! Or am I missing some property?

I am no expert in fourier analysis but can we interchange the use of the signs between the transform and the inverse transform?

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