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A decade ago, the mixed regularity of stationary many-body Schr\"o\-dingerequation has been studied by Harry Yserentant through the Pauli Principle andthe Hardy inequality (Uncertainty Principle). In this article, we prove thatthe many-body evolution Schr\"odinger equation has a similar mixed regularityif the initial data $u_0$ satisfies the Pauli Principle. By generalization ofthe Strichartz estimates, our method also applies to the numericalapproximation of this problem: based on these mixed derivatives, we design anew approximation which can hugely improve the computing capability especiallyin quantum chemistry.

Regularity of many-body Schr\"odinger evolution equation and its application to numerical analysis