I'd refer to a previous discussion 
https://groups.google.com/g/sympy/c/e8GiLUsr9eo/m/YKJ8sfHjBAAJ.

On Thursday, February 24, 2022 at 4:27:25 PM UTC+9 ranjithra...@gmail.com 
wrote:

> Dear all,
> I am new to this Google group.
>
>    - I have been using Python for 3 years.
>    - I am a PhD student working on superconductivity in 2D Topological 
>    materials(Physics). 
>    - I recently started using SymPy for some of my work mainly finding 
>    eigenvalues of Hamiltonian matrices. 
>    
> I noticed that *SymPy's Fourier transform function* does not work that 
> good when it comes to symbolic functions whose Fourier transforms result in 
> *Dirac-deltas 
> *despite having a delta function itself. eg: exp(-iat)or trigonometric 
> functions like sin(at) or cos(at). Mathematica does this fine and returns 
> expressions involving Dirac deltas. 
>
> If anyone has faced this problem before and found a solution, please 
> share. 
>

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