In this talk I present a way to transfer methods from signal processing, like the short-time Fourier transform or the wavelet transform and the respective reconstruction formulae, to the quantum setting. This approach works for discrete variables and continuous variables quantum systems. The focus is going to be on the operator short-time Fourier transform and the polarized Cohen’s class of an operator. This is joint work with Monika Doerfler, Henry McNulty and Eirik Skrettingland.

In this talk, I present my recent work with Simen Kvaal, where we developed a novel mathematical framework for density functional theory (DFT), the “gold standard method” used in large-scale many-particle quantum chemistry calculations. I present some preliminary results, where we address some open mathematical questions in DFT using our framework. 

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